4,299 views

All digital circuits can be realized using only

1. Ex-OR gates
2. Multiplexers
4. OR gates

### 1 comment

Half-Adder, and MUX both need help of constant 1, and can realize all logic circuits, hence B,C are the correct options.

### Subscribe to GO Classes for GATE CSE 2022

NOR gate, NAND gate, Multiplexers and Half adders can also be used to realise all digital circuits.

OR  gate?
edited
Corrected. NOR gate, NAND gate, Multiplexers and Half adders can also be used to realise all digital circuits.
Now? Or am I still missing something?
How possible with Half adder? We have an EXOR and AND gate. Can we make a NAND gate with this?
Yes, we can perform any operation using Half adder:

AND operation C = AB
NOT operation = S (with A and 1) = A⊕1 = A'.1+A.1' = A'
OR operation = ((A⊕1).(B⊕1))⊕1= (A'.B')' = A+B

AND followed by NOT will give NAND operation.

@Arjun Sir,

Half Adder is partially functionally complete not fully functionally complete.

I don't think they have used any Partially functional Complete term in Gate, So it is either complete or not complete.
So do we consider Half adder as functionally complete or not in GATE?
edited

@sambhrant , @vishalshrm539

find "It is not functionally complete then" on https://gateoverflow.in/157184/functionally-complete-sets

## So, most appropiate answer should be MULTIPLEXERS i.e. (b)

### Thanks :)

by

given the logic 0 and 1 as input , we can use half adders to compute any function
Even MUX requires, 0 and 1 inputs to be functionally complete.
@sushmita, Even multiplexer requires logic 0 & 1 to become functionally complete. Same is the case with half-adder. So why only multiplexer is answer?

@arjun sir, I feel answer by Rajarshi Sarkar should be the selected answer.
Only Mux is functionally complete.

Desired option Is only B..

# in this question if Sum expression and carry expression independently fuctionally complete then it is included my answer but in this case it is not possible my answer is Multiplexer

They didn't Ask you only functional complete

They just asking "All digital circuits can be realized using only"

so, here comes both partially FC and FC

So, Answer should be B and C