Logic gate: Logic gate is an electronic circuit that is used to take logical decisions based on the input. It contains one or more number of inputs and one output. The working of logic gate is based on the binary principle that has two states either logic 0 or logic 1. The output of logic gate is produced when it satisfies any of its logic conditions. The logic condition depends upon the type of the gates and the number of inputs. The primary logic gates include AND, OR and NOT and the combinations of these gates are used to implement any of the other logic gates. AND gate: The AND gate refers to a logic gate whose output will be HIGH only when all the inputs are HIGH. The output of AND gate will be LOW when any one of its input is LOW. The symbol to represent AND gate is given below. The truth table for AND gate is as follows. INPUT A INPUT B OUTPUT Y 0 0 0 0 1 0 1 0 0 1 1 1 OR gate: The OR gate refers to a logic gate whose output will be HIGH when any one of its inputs are HIGH. The output of AND gate will be LOW when both the inputs are LOW. The symbol to represent OR gate is given below. The truth table for OR gate is as follows. INPUT A INPUT B OUTPUT Y 0 0 0 0 1 1 1 0 1 1 1 1 NOT gate: The NOT gate refers to a logic gate whose output will be HIGH when it’s input is LOW and whose output will be LOW when it’s input is HIGH. The symbol to represent NOT gate is given below. The truth table for NOT gate is as follows. INPUT A OUTPUT Y 0 1 1 0

Question

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Answer 1

Question

Chapter 4, Problem 2P

Program Plan Intro

Logic gate:

Logic gate is an electronic circuit that is used to take logical decisions based on the input.

It contains one or more number of inputs and one output.

The working of logic gate is based on the binary principle that has two states either logic 0 or logic 1.

The output of logic gate is produced when it satisfies any of its logic conditions.

The logic condition depends upon the type of the gates and the number of inputs.

The primary logic gates include AND, OR and NOT and the combinations of these gates are used to implement any of the other logic gates.

AND gate:

The AND gate refers to a logic gate whose output will be HIGH only when all the inputs are HIGH.

The output of AND gate will be LOW when any one of its input is LOW.

The symbol to represent AND gate is given below.

The truth table for AND gate is as follows.

INPUT A INPUT B OUTPUT Y
0 0 0
0 1 0
1 0 0
1 1 1

OR gate:

The OR gate refers to a logic gate whose output will be HIGH when any one of its inputs are HIGH.

The output of AND gate will be LOW when both the inputs are LOW.

The symbol to represent OR gate is given below.

The truth table for OR gate is as follows.

INPUT A INPUT B OUTPUT Y
0 0 0
0 1 1
1 0 1
1 1 1

NOT gate:

The NOT gate refers to a logic gate whose output will be HIGH when it’s input is LOW and whose output will be LOW when it’s input is HIGH.

The symbol to represent NOT gate is given below.

The truth table for NOT gate is as follows.

INPUT A OUTPUT Y
0 1
1 0

Expert Solution

Explanation of Solution

a.

Logic gate circuit:

The logic gate circuit is as follows.

PROGRAMMABLE LOGIC CONTROL.(LL)>CUSTOM<, Chapter 4, Problem 2P , additional homework tip 4

Explanation:

In the above given logic gate circuit,

The inputs “A” and “B” are connected to logic OR gate and the corresponding output will be (A+B).
Now, the resultant along with other inputs “C” and “D” are connected to logic AND gate whose output will be $Y=(A+B)CD$ .

Therefore, the Boolean expression for the given logic circuit is $Y=(A+B)CD$ .

Explanation of Solution

b.

Logic gate circuit:

The logic gate circuit is as follows.

Explanation:

In the above given logic gate circuit,

The inputs “A” and “B” are connected to logic OR gate and the corresponding output will be (A+B).

The input “C” is connected to logic NOT gate and the corresponding output will be “ $C¯$ ”.

Then, the inputs “ $C¯$ ” and “D” are connected to another logic OR gate and the corresponding output will be $(C¯+D)$ .

Now, the output (A+B) and $(C¯+D)$ are connected to a logic AND gate whose output will be $Y=(A+B)(C¯+D)$ .

Therefore, the Boolean expression for the given logic circuit is $Y=(A+B)(C¯+D)$ .

Explanation of Solution

c.

Logic gate circuit:

The logic gate circuit is as follows.

Explanation:

In the above given logic gate circuit,

The inputs “A” and “B” are connected to logic AND gate and the corresponding output will be (AB).

Now, the resultant along with other input “C” is connected to logic OR gate whose output will be $Y=(AB+C)$ .

Therefore, the Boolean expression for the given logic circuit is $Y=(AB+C)$ .

Explanation of Solution

d.

Logic gate circuit:

The logic gate circuit is as follows.

Explanation:

In the above given logic gate circuit,

The inputs “A” and “B” are connected to logic AND gate and the corresponding output will be (AB).

Now, the resultant along with other input “C” is connected to logic OR gate whose output will be $(AB+C)$ .

The input “E” is connected to logic NOT gate and the corresponding output will be “ $E¯$ ”.

Now, the outputs $(AB+C)$ and $E¯$ along with the input “D” are connected to a logic AND gate whose output will be $Y=[(AB+C)DE¯]$ .

Therefore, the Boolean expression for the given logic circuit is $Y=[(AB+C)DE¯]$ .

Explanation of Solution

e.

Logic gate circuit:

The logic gate circuit is as follows.

Explanation:

In the above given logic gate circuit,

The inputs “A” and “B” are connected to logic OR gate and the corresponding output will be (A+B).

Then, the inputs “C” and “D” are connected to logic OR gate and the corresponding output will be $(C+D)$ .

Now, the output (A+B) and $(C+D)$ are connected to a logic AND gate whose output will be $Y=(A+B)(C+D)$ .

Therefore, the Boolean expression for the given logic circuit is $Y=(A+B)(C+D)$ .

Explanation of Solution

f.

Logic gate circuit:

The logic gate circuit is as follows.

Explanation:

In the above given logic gate circuit,

The input “B” is connected to logic NOT gate and the corresponding output will be “ $B¯$ ”.

The inputs “A” and “ $B¯$ ” are connected to logic AND gate and the corresponding output will be ( $AB¯$ ).

Similarly, the input “D” is connected to logic NOT gate and the corresponding output will be “ $D¯$ ”.

The inputs “C” and “ $D¯$ ” are connected to logic AND gate and the corresponding output will be ( $CD¯$ ).

Then, the input “F” is connected to logic NOT gate and the corresponding output will be “ $F¯$ ”.

The inputs “E” and “ $F¯$ ” are connected to logic AND gate and the corresponding output will be ( $EF¯$ ).

Finally, the outputs $AB¯$ , $CD¯$ and $EF¯$ are connected to a logic OR gate whose output will be $Y=(AB¯+CD¯+EF¯)$ .

Therefore, the Boolean expression for the given logic circuit is $Y=(AB¯+CD¯+EF¯)$ .

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Answer 2

Question

Chapter 4, Problem 2P

Program Plan Intro

Logic gate:

Logic gate is an electronic circuit that is used to take logical decisions based on the input.

It contains one or more number of inputs and one output.

The working of logic gate is based on the binary principle that has two states either logic 0 or logic 1.

The output of logic gate is produced when it satisfies any of its logic conditions.

The logic condition depends upon the type of the gates and the number of inputs.

The primary logic gates include AND, OR and NOT and the combinations of these gates are used to implement any of the other logic gates.

AND gate:

The AND gate refers to a logic gate whose output will be HIGH only when all the inputs are HIGH.

The output of AND gate will be LOW when any one of its input is LOW.

The symbol to represent AND gate is given below.

The truth table for AND gate is as follows.

INPUT A INPUT B OUTPUT Y
0 0 0
0 1 0
1 0 0
1 1 1

OR gate:

The OR gate refers to a logic gate whose output will be HIGH when any one of its inputs are HIGH.

The output of AND gate will be LOW when both the inputs are LOW.

The symbol to represent OR gate is given below.

The truth table for OR gate is as follows.

INPUT A INPUT B OUTPUT Y
0 0 0
0 1 1
1 0 1
1 1 1

NOT gate:

The NOT gate refers to a logic gate whose output will be HIGH when it’s input is LOW and whose output will be LOW when it’s input is HIGH.

The symbol to represent NOT gate is given below.

The truth table for NOT gate is as follows.

INPUT A OUTPUT Y
0 1
1 0

Expert Solution

Explanation of Solution

a.

Logic gate circuit:

The logic gate circuit is as follows.

PROGRAMMABLE LOGIC CONTROL.(LL)>CUSTOM<, Chapter 4, Problem 2P , additional homework tip 4

Explanation:

In the above given logic gate circuit,

The inputs “A” and “B” are connected to logic OR gate and the corresponding output will be (A+B).
Now, the resultant along with other inputs “C” and “D” are connected to logic AND gate whose output will be $Y=(A+B)CD$ .

Therefore, the Boolean expression for the given logic circuit is $Y=(A+B)CD$ .

Explanation of Solution

b.

Logic gate circuit:

The logic gate circuit is as follows.

Explanation:

In the above given logic gate circuit,

The inputs “A” and “B” are connected to logic OR gate and the corresponding output will be (A+B).

The input “C” is connected to logic NOT gate and the corresponding output will be “ $C¯$ ”.

Then, the inputs “ $C¯$ ” and “D” are connected to another logic OR gate and the corresponding output will be $(C¯+D)$ .

Now, the output (A+B) and $(C¯+D)$ are connected to a logic AND gate whose output will be $Y=(A+B)(C¯+D)$ .

Therefore, the Boolean expression for the given logic circuit is $Y=(A+B)(C¯+D)$ .

Explanation of Solution

c.

Logic gate circuit:

The logic gate circuit is as follows.

Explanation:

In the above given logic gate circuit,

The inputs “A” and “B” are connected to logic AND gate and the corresponding output will be (AB).

Now, the resultant along with other input “C” is connected to logic OR gate whose output will be $Y=(AB+C)$ .

Therefore, the Boolean expression for the given logic circuit is $Y=(AB+C)$ .

Explanation of Solution

d.

Logic gate circuit:

The logic gate circuit is as follows.

Explanation:

In the above given logic gate circuit,

The inputs “A” and “B” are connected to logic AND gate and the corresponding output will be (AB).

Now, the resultant along with other input “C” is connected to logic OR gate whose output will be $(AB+C)$ .

The input “E” is connected to logic NOT gate and the corresponding output will be “ $E¯$ ”.

Now, the outputs $(AB+C)$ and $E¯$ along with the input “D” are connected to a logic AND gate whose output will be $Y=[(AB+C)DE¯]$ .

Therefore, the Boolean expression for the given logic circuit is $Y=[(AB+C)DE¯]$ .

Explanation of Solution

e.

Logic gate circuit:

The logic gate circuit is as follows.

Explanation:

In the above given logic gate circuit,

The inputs “A” and “B” are connected to logic OR gate and the corresponding output will be (A+B).

Then, the inputs “C” and “D” are connected to logic OR gate and the corresponding output will be $(C+D)$ .

Now, the output (A+B) and $(C+D)$ are connected to a logic AND gate whose output will be $Y=(A+B)(C+D)$ .

Therefore, the Boolean expression for the given logic circuit is $Y=(A+B)(C+D)$ .

Explanation of Solution

f.

Logic gate circuit:

The logic gate circuit is as follows.

Explanation:

In the above given logic gate circuit,

The input “B” is connected to logic NOT gate and the corresponding output will be “ $B¯$ ”.

The inputs “A” and “ $B¯$ ” are connected to logic AND gate and the corresponding output will be ( $AB¯$ ).

Similarly, the input “D” is connected to logic NOT gate and the corresponding output will be “ $D¯$ ”.

The inputs “C” and “ $D¯$ ” are connected to logic AND gate and the corresponding output will be ( $CD¯$ ).

Then, the input “F” is connected to logic NOT gate and the corresponding output will be “ $F¯$ ”.

The inputs “E” and “ $F¯$ ” are connected to logic AND gate and the corresponding output will be ( $EF¯$ ).

Finally, the outputs $AB¯$ , $CD¯$ and $EF¯$ are connected to a logic OR gate whose output will be $Y=(AB¯+CD¯+EF¯)$ .

Therefore, the Boolean expression for the given logic circuit is $Y=(AB¯+CD¯+EF¯)$ .

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Answer 3

Question

Chapter 4, Problem 2P

Program Plan Intro

Logic gate:

Logic gate is an electronic circuit that is used to take logical decisions based on the input.

It contains one or more number of inputs and one output.

The working of logic gate is based on the binary principle that has two states either logic 0 or logic 1.

The output of logic gate is produced when it satisfies any of its logic conditions.

The logic condition depends upon the type of the gates and the number of inputs.

The primary logic gates include AND, OR and NOT and the combinations of these gates are used to implement any of the other logic gates.

AND gate:

The AND gate refers to a logic gate whose output will be HIGH only when all the inputs are HIGH.

The output of AND gate will be LOW when any one of its input is LOW.

The symbol to represent AND gate is given below.

The truth table for AND gate is as follows.

INPUT A INPUT B OUTPUT Y
0 0 0
0 1 0
1 0 0
1 1 1

OR gate:

The OR gate refers to a logic gate whose output will be HIGH when any one of its inputs are HIGH.

The output of AND gate will be LOW when both the inputs are LOW.

The symbol to represent OR gate is given below.

The truth table for OR gate is as follows.

INPUT A INPUT B OUTPUT Y
0 0 0
0 1 1
1 0 1
1 1 1

NOT gate:

The NOT gate refers to a logic gate whose output will be HIGH when it’s input is LOW and whose output will be LOW when it’s input is HIGH.

The symbol to represent NOT gate is given below.

The truth table for NOT gate is as follows.

INPUT A OUTPUT Y
0 1
1 0

Expert Solution

Explanation of Solution

a.

Logic gate circuit:

The logic gate circuit is as follows.

PROGRAMMABLE LOGIC CONTROL.(LL)>CUSTOM<, Chapter 4, Problem 2P , additional homework tip 4

Explanation:

In the above given logic gate circuit,

The inputs “A” and “B” are connected to logic OR gate and the corresponding output will be (A+B).
Now, the resultant along with other inputs “C” and “D” are connected to logic AND gate whose output will be $Y=(A+B)CD$ .

Therefore, the Boolean expression for the given logic circuit is $Y=(A+B)CD$ .

Explanation of Solution

b.

Logic gate circuit:

The logic gate circuit is as follows.

Explanation:

In the above given logic gate circuit,

The inputs “A” and “B” are connected to logic OR gate and the corresponding output will be (A+B).

The input “C” is connected to logic NOT gate and the corresponding output will be “ $C¯$ ”.

Then, the inputs “ $C¯$ ” and “D” are connected to another logic OR gate and the corresponding output will be $(C¯+D)$ .

Now, the output (A+B) and $(C¯+D)$ are connected to a logic AND gate whose output will be $Y=(A+B)(C¯+D)$ .

Therefore, the Boolean expression for the given logic circuit is $Y=(A+B)(C¯+D)$ .

Explanation of Solution

c.

Logic gate circuit:

The logic gate circuit is as follows.

Explanation:

In the above given logic gate circuit,

The inputs “A” and “B” are connected to logic AND gate and the corresponding output will be (AB).

Now, the resultant along with other input “C” is connected to logic OR gate whose output will be $Y=(AB+C)$ .

Therefore, the Boolean expression for the given logic circuit is $Y=(AB+C)$ .

Explanation of Solution

d.

Logic gate circuit:

The logic gate circuit is as follows.

Explanation:

In the above given logic gate circuit,

The inputs “A” and “B” are connected to logic AND gate and the corresponding output will be (AB).

Now, the resultant along with other input “C” is connected to logic OR gate whose output will be $(AB+C)$ .

The input “E” is connected to logic NOT gate and the corresponding output will be “ $E¯$ ”.

Now, the outputs $(AB+C)$ and $E¯$ along with the input “D” are connected to a logic AND gate whose output will be $Y=[(AB+C)DE¯]$ .

Therefore, the Boolean expression for the given logic circuit is $Y=[(AB+C)DE¯]$ .

Explanation of Solution

e.

Logic gate circuit:

The logic gate circuit is as follows.

Explanation:

In the above given logic gate circuit,

The inputs “A” and “B” are connected to logic OR gate and the corresponding output will be (A+B).

Then, the inputs “C” and “D” are connected to logic OR gate and the corresponding output will be $(C+D)$ .

Now, the output (A+B) and $(C+D)$ are connected to a logic AND gate whose output will be $Y=(A+B)(C+D)$ .

Therefore, the Boolean expression for the given logic circuit is $Y=(A+B)(C+D)$ .

Explanation of Solution

f.

Logic gate circuit:

The logic gate circuit is as follows.

Explanation:

In the above given logic gate circuit,

The input “B” is connected to logic NOT gate and the corresponding output will be “ $B¯$ ”.

The inputs “A” and “ $B¯$ ” are connected to logic AND gate and the corresponding output will be ( $AB¯$ ).

Similarly, the input “D” is connected to logic NOT gate and the corresponding output will be “ $D¯$ ”.

The inputs “C” and “ $D¯$ ” are connected to logic AND gate and the corresponding output will be ( $CD¯$ ).

Then, the input “F” is connected to logic NOT gate and the corresponding output will be “ $F¯$ ”.

The inputs “E” and “ $F¯$ ” are connected to logic AND gate and the corresponding output will be ( $EF¯$ ).

Finally, the outputs $AB¯$ , $CD¯$ and $EF¯$ are connected to a logic OR gate whose output will be $Y=(AB¯+CD¯+EF¯)$ .

Therefore, the Boolean expression for the given logic circuit is $Y=(AB¯+CD¯+EF¯)$ .

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Answer 4

Question

Chapter 4, Problem 2P

Program Plan Intro

Logic gate:

Logic gate is an electronic circuit that is used to take logical decisions based on the input.

It contains one or more number of inputs and one output.

The working of logic gate is based on the binary principle that has two states either logic 0 or logic 1.

The output of logic gate is produced when it satisfies any of its logic conditions.

The logic condition depends upon the type of the gates and the number of inputs.

The primary logic gates include AND, OR and NOT and the combinations of these gates are used to implement any of the other logic gates.

AND gate:

The AND gate refers to a logic gate whose output will be HIGH only when all the inputs are HIGH.

The output of AND gate will be LOW when any one of its input is LOW.

The symbol to represent AND gate is given below.

The truth table for AND gate is as follows.

INPUT A INPUT B OUTPUT Y
0 0 0
0 1 0
1 0 0
1 1 1

OR gate:

The OR gate refers to a logic gate whose output will be HIGH when any one of its inputs are HIGH.

The output of AND gate will be LOW when both the inputs are LOW.

The symbol to represent OR gate is given below.

The truth table for OR gate is as follows.

INPUT A INPUT B OUTPUT Y
0 0 0
0 1 1
1 0 1
1 1 1

NOT gate:

The NOT gate refers to a logic gate whose output will be HIGH when it’s input is LOW and whose output will be LOW when it’s input is HIGH.

The symbol to represent NOT gate is given below.

The truth table for NOT gate is as follows.

INPUT A OUTPUT Y
0 1
1 0

Expert Solution

Explanation of Solution

a.

Logic gate circuit:

The logic gate circuit is as follows.

PROGRAMMABLE LOGIC CONTROL.(LL)>CUSTOM<, Chapter 4, Problem 2P , additional homework tip 4

Explanation:

In the above given logic gate circuit,

The inputs “A” and “B” are connected to logic OR gate and the corresponding output will be (A+B).
Now, the resultant along with other inputs “C” and “D” are connected to logic AND gate whose output will be $Y=(A+B)CD$ .

Therefore, the Boolean expression for the given logic circuit is $Y=(A+B)CD$ .

Explanation of Solution

b.

Logic gate circuit:

The logic gate circuit is as follows.

Explanation:

In the above given logic gate circuit,

The inputs “A” and “B” are connected to logic OR gate and the corresponding output will be (A+B).

The input “C” is connected to logic NOT gate and the corresponding output will be “ $C¯$ ”.

Then, the inputs “ $C¯$ ” and “D” are connected to another logic OR gate and the corresponding output will be $(C¯+D)$ .

Now, the output (A+B) and $(C¯+D)$ are connected to a logic AND gate whose output will be $Y=(A+B)(C¯+D)$ .

Therefore, the Boolean expression for the given logic circuit is $Y=(A+B)(C¯+D)$ .

Explanation of Solution

c.

Logic gate circuit:

The logic gate circuit is as follows.

Explanation:

In the above given logic gate circuit,

The inputs “A” and “B” are connected to logic AND gate and the corresponding output will be (AB).

Now, the resultant along with other input “C” is connected to logic OR gate whose output will be $Y=(AB+C)$ .

Therefore, the Boolean expression for the given logic circuit is $Y=(AB+C)$ .

Explanation of Solution

d.

Logic gate circuit:

The logic gate circuit is as follows.

Explanation:

In the above given logic gate circuit,

The inputs “A” and “B” are connected to logic AND gate and the corresponding output will be (AB).

Now, the resultant along with other input “C” is connected to logic OR gate whose output will be $(AB+C)$ .

The input “E” is connected to logic NOT gate and the corresponding output will be “ $E¯$ ”.

Now, the outputs $(AB+C)$ and $E¯$ along with the input “D” are connected to a logic AND gate whose output will be $Y=[(AB+C)DE¯]$ .

Therefore, the Boolean expression for the given logic circuit is $Y=[(AB+C)DE¯]$ .

Explanation of Solution

e.

Logic gate circuit:

The logic gate circuit is as follows.

Explanation:

In the above given logic gate circuit,

The inputs “A” and “B” are connected to logic OR gate and the corresponding output will be (A+B).

Then, the inputs “C” and “D” are connected to logic OR gate and the corresponding output will be $(C+D)$ .

Now, the output (A+B) and $(C+D)$ are connected to a logic AND gate whose output will be $Y=(A+B)(C+D)$ .

Therefore, the Boolean expression for the given logic circuit is $Y=(A+B)(C+D)$ .

Explanation of Solution

f.

Logic gate circuit:

The logic gate circuit is as follows.

Explanation:

In the above given logic gate circuit,

The input “B” is connected to logic NOT gate and the corresponding output will be “ $B¯$ ”.

The inputs “A” and “ $B¯$ ” are connected to logic AND gate and the corresponding output will be ( $AB¯$ ).

Similarly, the input “D” is connected to logic NOT gate and the corresponding output will be “ $D¯$ ”.

The inputs “C” and “ $D¯$ ” are connected to logic AND gate and the corresponding output will be ( $CD¯$ ).

Then, the input “F” is connected to logic NOT gate and the corresponding output will be “ $F¯$ ”.

The inputs “E” and “ $F¯$ ” are connected to logic AND gate and the corresponding output will be ( $EF¯$ ).

Finally, the outputs $AB¯$ , $CD¯$ and $EF¯$ are connected to a logic OR gate whose output will be $Y=(AB¯+CD¯+EF¯)$ .

Therefore, the Boolean expression for the given logic circuit is $Y=(AB¯+CD¯+EF¯)$ .

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Answer 5

Chapter 4, Problem 2P

Program Plan Intro

Logic gate:

Logic gate is an electronic circuit that is used to take logical decisions based on the input.

It contains one or more number of inputs and one output.

The working of logic gate is based on the binary principle that has two states either logic 0 or logic 1.

The output of logic gate is produced when it satisfies any of its logic conditions.

The logic condition depends upon the type of the gates and the number of inputs.

The primary logic gates include AND, OR and NOT and the combinations of these gates are used to implement any of the other logic gates.

AND gate:

The AND gate refers to a logic gate whose output will be HIGH only when all the inputs are HIGH.

The output of AND gate will be LOW when any one of its input is LOW.

The symbol to represent AND gate is given below.

The truth table for AND gate is as follows.

INPUT A INPUT B OUTPUT Y
0 0 0
0 1 0
1 0 0
1 1 1

OR gate:

The OR gate refers to a logic gate whose output will be HIGH when any one of its inputs are HIGH.

The output of AND gate will be LOW when both the inputs are LOW.

The symbol to represent OR gate is given below.

The truth table for OR gate is as follows.

INPUT A INPUT B OUTPUT Y
0 0 0
0 1 1
1 0 1
1 1 1

NOT gate:

The NOT gate refers to a logic gate whose output will be HIGH when it’s input is LOW and whose output will be LOW when it’s input is HIGH.

The symbol to represent NOT gate is given below.

The truth table for NOT gate is as follows.

INPUT A OUTPUT Y
0 1
1 0

Expert Solution

Explanation of Solution

a.

Logic gate circuit:

The logic gate circuit is as follows.

PROGRAMMABLE LOGIC CONTROL.(LL)>CUSTOM<, Chapter 4, Problem 2P , additional homework tip 4

Explanation:

In the above given logic gate circuit,

The inputs “A” and “B” are connected to logic OR gate and the corresponding output will be (A+B).
Now, the resultant along with other inputs “C” and “D” are connected to logic AND gate whose output will be $Y=(A+B)CD$ .

Therefore, the Boolean expression for the given logic circuit is $Y=(A+B)CD$ .

Explanation of Solution

b.

Logic gate circuit:

The logic gate circuit is as follows.

Explanation:

In the above given logic gate circuit,

The inputs “A” and “B” are connected to logic OR gate and the corresponding output will be (A+B).

The input “C” is connected to logic NOT gate and the corresponding output will be “ $C¯$ ”.

Then, the inputs “ $C¯$ ” and “D” are connected to another logic OR gate and the corresponding output will be $(C¯+D)$ .

Now, the output (A+B) and $(C¯+D)$ are connected to a logic AND gate whose output will be $Y=(A+B)(C¯+D)$ .

Therefore, the Boolean expression for the given logic circuit is $Y=(A+B)(C¯+D)$ .

Explanation of Solution

c.

Logic gate circuit:

The logic gate circuit is as follows.

Explanation:

In the above given logic gate circuit,

The inputs “A” and “B” are connected to logic AND gate and the corresponding output will be (AB).

Now, the resultant along with other input “C” is connected to logic OR gate whose output will be $Y=(AB+C)$ .

Therefore, the Boolean expression for the given logic circuit is $Y=(AB+C)$ .

Explanation of Solution

d.

Logic gate circuit:

The logic gate circuit is as follows.

Explanation:

In the above given logic gate circuit,

The inputs “A” and “B” are connected to logic AND gate and the corresponding output will be (AB).

Now, the resultant along with other input “C” is connected to logic OR gate whose output will be $(AB+C)$ .

The input “E” is connected to logic NOT gate and the corresponding output will be “ $E¯$ ”.

Now, the outputs $(AB+C)$ and $E¯$ along with the input “D” are connected to a logic AND gate whose output will be $Y=[(AB+C)DE¯]$ .

Therefore, the Boolean expression for the given logic circuit is $Y=[(AB+C)DE¯]$ .

Explanation of Solution

e.

Logic gate circuit:

The logic gate circuit is as follows.

Explanation:

In the above given logic gate circuit,

The inputs “A” and “B” are connected to logic OR gate and the corresponding output will be (A+B).

Then, the inputs “C” and “D” are connected to logic OR gate and the corresponding output will be $(C+D)$ .

Now, the output (A+B) and $(C+D)$ are connected to a logic AND gate whose output will be $Y=(A+B)(C+D)$ .

Therefore, the Boolean expression for the given logic circuit is $Y=(A+B)(C+D)$ .

Explanation of Solution

f.

Logic gate circuit:

The logic gate circuit is as follows.

Explanation:

In the above given logic gate circuit,

The input “B” is connected to logic NOT gate and the corresponding output will be “ $B¯$ ”.

The inputs “A” and “ $B¯$ ” are connected to logic AND gate and the corresponding output will be ( $AB¯$ ).

Similarly, the input “D” is connected to logic NOT gate and the corresponding output will be “ $D¯$ ”.

The inputs “C” and “ $D¯$ ” are connected to logic AND gate and the corresponding output will be ( $CD¯$ ).

Then, the input “F” is connected to logic NOT gate and the corresponding output will be “ $F¯$ ”.

The inputs “E” and “ $F¯$ ” are connected to logic AND gate and the corresponding output will be ( $EF¯$ ).

Finally, the outputs $AB¯$ , $CD¯$ and $EF¯$ are connected to a logic OR gate whose output will be $Y=(AB¯+CD¯+EF¯)$ .

Therefore, the Boolean expression for the given logic circuit is $Y=(AB¯+CD¯+EF¯)$ .

Answer 6

Chapter 4, Problem 2P

Program Plan Intro

Logic gate:

Logic gate is an electronic circuit that is used to take logical decisions based on the input.

It contains one or more number of inputs and one output.

The working of logic gate is based on the binary principle that has two states either logic 0 or logic 1.

The output of logic gate is produced when it satisfies any of its logic conditions.

The logic condition depends upon the type of the gates and the number of inputs.

The primary logic gates include AND, OR and NOT and the combinations of these gates are used to implement any of the other logic gates.

AND gate:

The AND gate refers to a logic gate whose output will be HIGH only when all the inputs are HIGH.

The output of AND gate will be LOW when any one of its input is LOW.

The symbol to represent AND gate is given below.

The truth table for AND gate is as follows.

INPUT A INPUT B OUTPUT Y
0 0 0
0 1 0
1 0 0
1 1 1

OR gate:

The OR gate refers to a logic gate whose output will be HIGH when any one of its inputs are HIGH.

The output of AND gate will be LOW when both the inputs are LOW.

The symbol to represent OR gate is given below.

The truth table for OR gate is as follows.

INPUT A INPUT B OUTPUT Y
0 0 0
0 1 1
1 0 1
1 1 1

NOT gate:

The NOT gate refers to a logic gate whose output will be HIGH when it’s input is LOW and whose output will be LOW when it’s input is HIGH.

The symbol to represent NOT gate is given below.

The truth table for NOT gate is as follows.

INPUT A OUTPUT Y
0 1
1 0

Expert Solution

Explanation of Solution

a.

Logic gate circuit:

The logic gate circuit is as follows.

PROGRAMMABLE LOGIC CONTROL.(LL)>CUSTOM<, Chapter 4, Problem 2P , additional homework tip 4

Explanation:

In the above given logic gate circuit,

The inputs “A” and “B” are connected to logic OR gate and the corresponding output will be (A+B).
Now, the resultant along with other inputs “C” and “D” are connected to logic AND gate whose output will be $Y=(A+B)CD$ .

Therefore, the Boolean expression for the given logic circuit is $Y=(A+B)CD$ .

Answer 7

Chapter 4, Problem 2P

Program Plan Intro

Logic gate:

Logic gate is an electronic circuit that is used to take logical decisions based on the input.

It contains one or more number of inputs and one output.

The working of logic gate is based on the binary principle that has two states either logic 0 or logic 1.

The output of logic gate is produced when it satisfies any of its logic conditions.

The logic condition depends upon the type of the gates and the number of inputs.

The primary logic gates include AND, OR and NOT and the combinations of these gates are used to implement any of the other logic gates.

AND gate:

The AND gate refers to a logic gate whose output will be HIGH only when all the inputs are HIGH.

The output of AND gate will be LOW when any one of its input is LOW.

The symbol to represent AND gate is given below.

The truth table for AND gate is as follows.

INPUT A INPUT B OUTPUT Y
0 0 0
0 1 0
1 0 0
1 1 1

OR gate:

The OR gate refers to a logic gate whose output will be HIGH when any one of its inputs are HIGH.

The output of AND gate will be LOW when both the inputs are LOW.

The symbol to represent OR gate is given below.

The truth table for OR gate is as follows.

INPUT A INPUT B OUTPUT Y
0 0 0
0 1 1
1 0 1
1 1 1

NOT gate:

The NOT gate refers to a logic gate whose output will be HIGH when it’s input is LOW and whose output will be LOW when it’s input is HIGH.

The symbol to represent NOT gate is given below.

The truth table for NOT gate is as follows.

INPUT A OUTPUT Y
0 1
1 0

Answer 8

Expert Solution

Explanation of Solution

a.

Logic gate circuit:

The logic gate circuit is as follows.

PROGRAMMABLE LOGIC CONTROL.(LL)>CUSTOM<, Chapter 4, Problem 2P , additional homework tip 4

Explanation:

In the above given logic gate circuit,

The inputs “A” and “B” are connected to logic OR gate and the corresponding output will be (A+B).
Now, the resultant along with other inputs “C” and “D” are connected to logic AND gate whose output will be $Y=(A+B)CD$ .

Therefore, the Boolean expression for the given logic circuit is $Y=(A+B)CD$ .

Answer 9

Expert Solution

Answer 10

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

b.

Logic gate circuit:

The logic gate circuit is as follows.

Explanation:

In the above given logic gate circuit,

The inputs “A” and “B” are connected to logic OR gate and the corresponding output will be (A+B).

The input “C” is connected to logic NOT gate and the corresponding output will be “ $C¯$ ”.

Then, the inputs “ $C¯$ ” and “D” are connected to another logic OR gate and the corresponding output will be $(C¯+D)$ .

Now, the output (A+B) and $(C¯+D)$ are connected to a logic AND gate whose output will be $Y=(A+B)(C¯+D)$ .

Therefore, the Boolean expression for the given logic circuit is $Y=(A+B)(C¯+D)$ .

Answer 13

Explanation of Solution

b.

Logic gate circuit:

The logic gate circuit is as follows.

Explanation:

In the above given logic gate circuit,

The inputs “A” and “B” are connected to logic OR gate and the corresponding output will be (A+B).

The input “C” is connected to logic NOT gate and the corresponding output will be “ $C¯$ ”.

Then, the inputs “ $C¯$ ” and “D” are connected to another logic OR gate and the corresponding output will be $(C¯+D)$ .

Now, the output (A+B) and $(C¯+D)$ are connected to a logic AND gate whose output will be $Y=(A+B)(C¯+D)$ .

Therefore, the Boolean expression for the given logic circuit is $Y=(A+B)(C¯+D)$ .

Answer 14

Explanation of Solution

c.

Logic gate circuit:

The logic gate circuit is as follows.

Explanation:

In the above given logic gate circuit,

The inputs “A” and “B” are connected to logic AND gate and the corresponding output will be (AB).

Now, the resultant along with other input “C” is connected to logic OR gate whose output will be $Y=(AB+C)$ .

Therefore, the Boolean expression for the given logic circuit is $Y=(AB+C)$ .

Answer 15

Explanation of Solution

c.

Logic gate circuit:

The logic gate circuit is as follows.

Explanation:

In the above given logic gate circuit,

The inputs “A” and “B” are connected to logic AND gate and the corresponding output will be (AB).

Now, the resultant along with other input “C” is connected to logic OR gate whose output will be $Y=(AB+C)$ .

Therefore, the Boolean expression for the given logic circuit is $Y=(AB+C)$ .

Answer 16

Explanation of Solution

d.

Logic gate circuit:

The logic gate circuit is as follows.

Explanation:

In the above given logic gate circuit,

The inputs “A” and “B” are connected to logic AND gate and the corresponding output will be (AB).

Now, the resultant along with other input “C” is connected to logic OR gate whose output will be $(AB+C)$ .

The input “E” is connected to logic NOT gate and the corresponding output will be “ $E¯$ ”.

Now, the outputs $(AB+C)$ and $E¯$ along with the input “D” are connected to a logic AND gate whose output will be $Y=[(AB+C)DE¯]$ .

Therefore, the Boolean expression for the given logic circuit is $Y=[(AB+C)DE¯]$ .

Answer 17

Explanation of Solution

d.

Logic gate circuit:

The logic gate circuit is as follows.

Explanation:

In the above given logic gate circuit,

The inputs “A” and “B” are connected to logic AND gate and the corresponding output will be (AB).

Now, the resultant along with other input “C” is connected to logic OR gate whose output will be $(AB+C)$ .

The input “E” is connected to logic NOT gate and the corresponding output will be “ $E¯$ ”.

Now, the outputs $(AB+C)$ and $E¯$ along with the input “D” are connected to a logic AND gate whose output will be $Y=[(AB+C)DE¯]$ .

Therefore, the Boolean expression for the given logic circuit is $Y=[(AB+C)DE¯]$ .

Answer 18

Explanation of Solution

e.

Logic gate circuit:

The logic gate circuit is as follows.

Explanation:

In the above given logic gate circuit,

The inputs “A” and “B” are connected to logic OR gate and the corresponding output will be (A+B).

Then, the inputs “C” and “D” are connected to logic OR gate and the corresponding output will be $(C+D)$ .

Now, the output (A+B) and $(C+D)$ are connected to a logic AND gate whose output will be $Y=(A+B)(C+D)$ .

Therefore, the Boolean expression for the given logic circuit is $Y=(A+B)(C+D)$ .

Answer 19

Explanation of Solution

e.

Logic gate circuit:

The logic gate circuit is as follows.

Explanation:

In the above given logic gate circuit,

The inputs “A” and “B” are connected to logic OR gate and the corresponding output will be (A+B).

Then, the inputs “C” and “D” are connected to logic OR gate and the corresponding output will be $(C+D)$ .

Now, the output (A+B) and $(C+D)$ are connected to a logic AND gate whose output will be $Y=(A+B)(C+D)$ .

Therefore, the Boolean expression for the given logic circuit is $Y=(A+B)(C+D)$ .

Answer 20

Explanation of Solution

f.

Logic gate circuit:

The logic gate circuit is as follows.

Explanation:

In the above given logic gate circuit,

The input “B” is connected to logic NOT gate and the corresponding output will be “ $B¯$ ”.

The inputs “A” and “ $B¯$ ” are connected to logic AND gate and the corresponding output will be ( $AB¯$ ).

Similarly, the input “D” is connected to logic NOT gate and the corresponding output will be “ $D¯$ ”.

The inputs “C” and “ $D¯$ ” are connected to logic AND gate and the corresponding output will be ( $CD¯$ ).

Then, the input “F” is connected to logic NOT gate and the corresponding output will be “ $F¯$ ”.

The inputs “E” and “ $F¯$ ” are connected to logic AND gate and the corresponding output will be ( $EF¯$ ).

Finally, the outputs $AB¯$ , $CD¯$ and $EF¯$ are connected to a logic OR gate whose output will be $Y=(AB¯+CD¯+EF¯)$ .

Therefore, the Boolean expression for the given logic circuit is $Y=(AB¯+CD¯+EF¯)$ .

Answer 21

Explanation of Solution

f.

Logic gate circuit:

The logic gate circuit is as follows.

Explanation:

In the above given logic gate circuit,

The input “B” is connected to logic NOT gate and the corresponding output will be “ $B¯$ ”.

The inputs “A” and “ $B¯$ ” are connected to logic AND gate and the corresponding output will be ( $AB¯$ ).

Similarly, the input “D” is connected to logic NOT gate and the corresponding output will be “ $D¯$ ”.

The inputs “C” and “ $D¯$ ” are connected to logic AND gate and the corresponding output will be ( $CD¯$ ).

Then, the input “F” is connected to logic NOT gate and the corresponding output will be “ $F¯$ ”.

The inputs “E” and “ $F¯$ ” are connected to logic AND gate and the corresponding output will be ( $EF¯$ ).

Finally, the outputs $AB¯$ , $CD¯$ and $EF¯$ are connected to a logic OR gate whose output will be $Y=(AB¯+CD¯+EF¯)$ .

Therefore, the Boolean expression for the given logic circuit is $Y=(AB¯+CD¯+EF¯)$ .

Answer 22

Ch. 4 - Prob. 1RQ Ch. 4 - Prob. 2RQ Ch. 4 - Draw the logic symbol, construct a truth table,...Ch. 4 - Express each of the following equations as a...Ch. 4 - Prob. 5RQ Ch. 4 - Prob. 6RQ Ch. 4 - State the logic instruction you would use when you...Ch. 4 - Prob. 8RQ Ch. 4 - Prob. 9RQ Ch. 4 - Prob. 1P

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Chapter 4 Solutions

INPUT A	INPUT B	OUTPUT Y
0	0	0
0	1	0
1	0	0
1	1	1

INPUT A	INPUT B	OUTPUT Y
0	0	0
0	1	1
1	0	1
1	1	1

INPUT A	OUTPUT Y
0	1
1	0