Consider the following circuit

The function by the network above is

Question

Question

This question was previously asked in

ISRO Scientist CS 2020 Official Paper

Answer 1

Level 1:

Output of NAND $\overset{―}{A B}$

Output of NOR $\overset{―}{C + D}$

Level 2:

Output of 1^st AND - $\overset{―}{A B .} E$

Output of 2^nd AND –

Output of 3^rd AND – ( $\overset{―}{C + D}) F$

Level 3:

Final Output is ‘NOR’ all the AND outputs obtained above

$\overset{―}{\overset{―}{A B .} E + E F + \overset{―}{(C + D)} F}$

Distributing the bar separately, we get

$\overset{―}{\overset{―}{A . B} . E} . \overset{―}{E F} . \overset{―}{\overset{―}{(C + D)} . F}$ ))

Using De Morgan’s law, we get

$(A B + \bar{E}) (\bar{E} + \bar{F}) (C + D + \bar{F})$

$(A B \bar{E} + A B \bar{F} + \bar{E} + \bar{E} . \bar{F}) (C + D + \bar{F})$

$(\bar{E} (A B + 1 + \bar{F}) + A B \bar{F}) (C + D + \bar{F})$

$(\bar{E} + A B \bar{F}) (C + D + \bar{F})$