Page 88 - Computer Science V2.0 Class 11

3.4.2 Additional Logic Gates
Multiple input gates: Consider the boolean function F = (x ● y) ● z. Fig 3.5 shows an implementation of the
Boolean function F = (x ● y) ● z. using two AND gates.

x
y

F = (x ● y) ● z

z

Fig 3.5: Logic Diagram for Boolean function F = (x ● y) ● z
We often use multiple input AND and OR gates to simplify the logic diagrams. For example, Fig 3.5 may be simplified
using a three input AND gate shown in Fig 3.6

x
y F = x ● y ● z
z

Fig 3.6: Simplified Logic Diagram for Boolean function F = x ● y ● z
NAND gate: NAND gate has the effect of applying an AND gate, followed by a NOT gate. Thus, A NAND B is equivalent to
(A●B)'. The truth table and logic diagram for NAND gate are given in Table 3.8 and Fig 3.7, respectively.

A B (A ● B)'
0 0 1
0 1 1
1 0 1

1 1 0
Table 3.8 Truth table for NAND gate

A
A NAND B

B
Fig 3.7: Logic Diagram for NAND gate
By De Morgan's law of Boolean algebra; we know that (A ● B)'= A' + B'. So, a NAND gate may also be implemented
by negating the inputs, followed by the application of an OR gate as shown in Fig 3.9.

Fig 3.8: Logic Diagram for NAND gate Fig 3.9: Logic Diagram for NAND gate
NOR gate: NOR gate has the effect of applying an OR gate, followed by a NOT gate. Thus, A NOR B is equivalent to
(A + B)'. The truth table and logic diagram for NOR gate are shown in Table 3.9 and Fig 3.10, respectively.

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