Page 89 - Computer Science V2.0 Class 11

A B (A + B)'
0 0 1
0 1 0
1 0 0
1 1 0
Table 3.9: Truth table for NOR gate

A
A NOR B
B

Fig 3.10: Logic Diagram for NOR gate
Again, by De Morgan's law of Boolean algebra, we know that (A + B)'= A' ● B'. So, a NOR gate may be implemented
by negating the inputs, followed by the application of an AND gate as shown in Fig 3.12.

Fig 3.11: Logic Diagram for NOR gate Fig 3.12: Logic Diagram for NOR gate
XOR gate: The effect of the exclusive – OR (abbreviated as XOR, also denoted by ⊕) gate is defined by the equation
A XOR B = AB' + BA'. The truth table and logic diagram for the XOR gate are shown in Table 3.10 and Fig 3.13, respectively.

A B A XOR B

0 0 0 A
0 1 1
( A ● B) + (A ● B ) = A ⊕ B
1 0 1
1 1 0 B
Table 3.10: Truth table for XOR gate Fig 3.13: Logic Diagram for XOR gate

Note that A XOR B = 1 if and only if exactly one of A and B is equal to 1 and the other is equal to 0. If A and B have the
same value (0 or 1), A XOR B becomes 0. An XOR gate is denoted by the symbol shown in Fig 3.14.

Fig 3.14: Logic Diagram for XOR gate
Equivalence gate: The effect of the equivalence gate, also called exclusive NOR gate (abbreviated as X-NOR) is defined
by the equation A X–NOR B = AꞌBꞌ + AB. So, an equivalence gate outputs 1 if both the inputs are same
(either both equal to 1 or both equal to 0) and 0 otherwise. The symbol used for equivalence gate is shown in Fig 3.15.

Fig 3.15: Logic Diagram for X-NOR gate

Boolean Logic 75