25 votes 25 votes All digital circuits can be realized using only Ex-OR gates Multiplexers Half adders OR gates Digital Logic gate1992 normal digital-logic digital-circuits multiple-selects functional-completeness combinational-circuit + – Kathleen asked Sep 12, 2014 • retagged Oct 21, 2023 by Deepak Poonia Kathleen 10.6k views answer comment Share Follow See 1 comment See all 1 1 comment reply chauhansunil20th commented Nov 13, 2018 reply Follow Share Half-Adder, and MUX both need help of constant 1, and can realize all logic circuits, hence B,C are the correct options. 1 votes 1 votes Please log in or register to add a comment.
Best answer 25 votes 25 votes Answer: B, C NOR gate, NAND gate, Multiplexers and Half adders can also be used to realise all digital circuits. Rajarshi Sarkar answered Apr 25, 2015 • selected Jan 17, 2018 by rahul sharma 5 Rajarshi Sarkar comment Share Follow See all 10 Comments See all 10 10 Comments reply Arjun commented Apr 25, 2015 reply Follow Share OR gate? 0 votes 0 votes Rajarshi Sarkar commented Apr 25, 2015 i edited by Rajarshi Sarkar Apr 26, 2015 reply Follow Share Corrected. NOR gate, NAND gate, Multiplexers and Half adders can also be used to realise all digital circuits. 2 votes 2 votes Rajarshi Sarkar commented Apr 26, 2015 reply Follow Share Now? Or am I still missing something? 1 votes 1 votes Arjun commented Apr 26, 2015 reply Follow Share How possible with Half adder? We have an EXOR and AND gate. Can we make a NAND gate with this? 1 votes 1 votes Rajarshi Sarkar commented Apr 26, 2015 reply Follow Share 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. 31 votes 31 votes Nishant Arora commented Dec 19, 2016 reply Follow Share @arjun sir here XOR with AND not given functionally complet.. http://math.stackexchange.com/questions/331974/implement-using-only-xor-gates-f-abcdabcdabcdabcdabcd 1 votes 1 votes Shubhanshu commented Sep 30, 2017 reply Follow Share @Rajarshi Sarkar @Arjun Sir, Half Adder is partially functionally complete not fully functionally complete. 4 votes 4 votes vishalshrm539 commented Nov 1, 2018 reply Follow Share I don't think they have used any Partially functional Complete term in Gate, So it is either complete or not complete. 2 votes 2 votes Sambhrant Maurya commented Jul 3, 2019 reply Follow Share So do we consider Half adder as functionally complete or not in GATE? 1 votes 1 votes Adarsh Pandey commented Jul 22, 2020 i edited by Adarsh Pandey Jul 22, 2020 reply Follow Share @sambhrant , @vishalshrm539 find "It is not functionally complete then" on https://gateoverflow.in/157184/functionally-complete-sets 0 votes 0 votes Please log in or register to add a comment.
11 votes 11 votes Half adders are not fully functionally complete they are partially functionally complete. So, most appropiate answer should be MULTIPLEXERS i.e. (b) Thanks :) Harit answered Jan 2, 2017 Harit comment Share Follow See all 3 Comments See all 3 3 Comments reply Niraj Singh 2 commented Dec 13, 2017 reply Follow Share given the logic 0 and 1 as input , we can use half adders to compute any function 0 votes 0 votes krish__ commented Dec 21, 2017 reply Follow Share Even MUX requires, 0 and 1 inputs to be functionally complete. 8 votes 8 votes Churchill Khangar commented Dec 29, 2017 reply Follow Share @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. 1 votes 1 votes Please log in or register to add a comment.
2 votes 2 votes 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 shaktisingh answered Nov 21, 2019 shaktisingh comment Share Follow See all 0 reply Please log in or register to add a comment.
1 votes 1 votes Only Mux is functionally complete. Desired option Is only B.. akash.dinkar12 answered May 21, 2017 akash.dinkar12 comment Share Follow See 1 comment See all 1 1 comment reply Chandrabhan Vishwa 1 commented Dec 13, 2017 reply Follow Share in case of half adder sum =AxorB and Carry=AB 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 0 votes 0 votes Please log in or register to add a comment.