You are given two circuits as shown in Fig. 14.46, which consistof NAND gates. Identify the logic operation carried out by the twocircuits.
Given: A and B acts as the Two inputs of the circuit Y is the output.
a)
Let left side of the output is given as, Y 1 .
The output of the left of the NAND gate is given as,
Y 1 = A ⋅ B ¯
This output is fed through the another NAND Gate.
The circuit output is given as,
Y = Y 1 ⋅ Y 1 ¯
Substitute the value of Y 1 in above expression,
Y = ( A ⋅ B ¯ ) ⋅ ( A ⋅ B ¯ ) ¯ = ( AB ¯ ) ¯ + ( AB ¯ ) ¯ = AB
Thus, the circuit acts as AND Gate.
b)
A ¯ is output of the upper left of the NAND gate and B ¯ is the output of the lower half of the NAND gate.
The output of the circuit is given as,
Y = A ¯ ⋅ B ¯ = A ¯ ¯ + B ¯ ¯ = A + B
Thus, the circuit acts as OR gate.
Given: A and B acts as the Two inputs of the circuit Y is the output.
a)
Let left side of the output is given as,
The output of the left of the NAND gate is given as,
This output is fed through the another NAND Gate.
The circuit output is given as,
Substitute the value of
Thus, the circuit acts as AND Gate.
b)
The output of the circuit is given as,
Thus, the circuit acts as OR gate.
