AND gate: The AND gate is denoted by “AND”, “.” or no symbol. The AND gate is always opposite to the OR gate. Truth table: Consider the truth table of AND gate is as follows: A B C = AB 0 0 0 0 1 0 1 0 0 1 1 1 Here, the Boolean expressions “AB” is equivalent to the expression “A.B” is read “A and B”. The result of the given expression is 1 only when both the inputs are 1, and 0 otherwise. OR gate: The OR gate is denoted by “OR” or “+”. The result of OR gate is 0 when both the inputs are 0, otherwise 1. Truth table: Consider the truth table of OR gate is as follows: A B C = A+B 0 0 0 0 1 1 1 0 1 1 1 1 Here, the Boolean expressions “A+B” then it is read “A or B”. The result of the given expression is 0 only when both the inputs are 0, and 1 otherwise. NOT gate: The NOT gate denoted by negation symbol like “B’”. The result of NOT gate is 0 if the input is 1 and vice versa. Truth table: The truth table for NOT gate is given below: A B' 0 1 1 0 Here, the “B’” is simply opposite value of the input variable “A”. Ex-OR gate: The result of Ex-OR gate will be 1, if any of the input is 0. Otherwise 1. The truth table for XOR gate is given below: A B C = A ⊕ B 0 0 0 0 1 1 1 0 1 1 1 0 Here, the Boolean expression of “A ⊕ B” gives 0 if both the inputs are 1 or 0 and 0 if any one of the input is 1. NAND gate: The NAND gate is always opposite to the AND gate which means the result of NAND gate is 0 if both inputs are 1, otherwise 0. Truth table: Consider the truth table of NAND gate is as follows: A B C = (AB)’ 0 0 1 0 1 1 1 0 1 1 1 0 The result of the given expression is 0 only when both the inputs are 1, and 0 otherwise.

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Chapter 3, Problem 38E

Program Plan Intro

AND gate:

The AND gate is denoted by “AND”, “.” or no symbol. The AND gate is always opposite to the OR gate.

Truth table:

Consider the truth table of AND gate is as follows:

A B C = AB
0 0 0
0 1 0
1 0 0
1 1 1

Here, the Boolean expressions “AB” is equivalent to the expression “A.B” is read “A and B”. The result of the given expression is 1 only when both the inputs are 1, and 0 otherwise.

OR gate:

The OR gate is denoted by “OR” or “+”. The result of OR gate is 0 when both the inputs are 0, otherwise 1.

Truth table:

Consider the truth table of OR gate is as follows:

A B C = A+B
0 0 0
0 1 1
1 0 1
1 1 1

Here, the Boolean expressions “A+B” then it is read “A or B”. The result of the given expression is 0 only when both the inputs are 0, and 1 otherwise.

NOT gate:

The NOT gate denoted by negation symbol like “B’”. The result of NOT gate is 0 if the input is 1 and vice versa.

Truth table:

The truth table for NOT gate is given below:

A B'
0 1
1 0

Here, the “B’” is simply opposite value of the input variable “A”.

Ex-OR gate:

The result of Ex-OR gate will be 1, if any of the input is 0. Otherwise 1.

The truth table for XOR gate is given below:

A B C = A ⊕ B
0 0 0
0 1 1
1 0 1
1 1 0

Here, the Boolean expression of “A ⊕ B” gives 0 if both the inputs are 1 or 0 and 0 if any one of the input is 1.

NAND gate:

The NAND gate is always opposite to the AND gate which means the result of NAND gate is 0 if both inputs are 1, otherwise 0.

Truth table:

Consider the truth table of NAND gate is as follows:

A B C = (AB)’
0 0 1
0 1 1
1 0 1
1 1 0

The result of the given expression is 0 only when both the inputs are 1, and 0 otherwise.

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