Chapter 3, Problem 50E

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 $\oplus$ B
0	0	0
0	1	1
1	0	1
1	1	0

 Here, the Boolean expression of “A $\oplus$ 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.