Computing

126 ◾ Computing

expressed by using only NOR gates, and also can be expressed by using only

NAND gates. e NOR gate is a Boolean function

fxxxx(,)( )

12

12

=¬ ∨

,

and the NOT gate is a Boolean function

fxxxx(,)( )

12

12

=¬ ∧

. e truth

tables of the NOR gate and the NAND gate are given in Table15.3.

Example 15.4

Let the NOR of x and y, and the NAND of x and y be expressed by

NOR(x,y) and NAND(x,y), respectively. en the OR gate, AND gate,

and NOT gate can each be expressed by using only NOR gates, as well

as by using only NAND gates, as shown below:

x∨y = NOR(NOR(x,y), NOR(x,y)) = NAND(NAND(x,x), NAND(y,y))

x∧y = NOR(NOR(x,x), NOR(y,y)) = NAND(