The Gateway to Computer Science Excellence
+18 votes

What is the boolean expression for the output $f$ of the combinational logic circuit of NOR gates given below?

  1. $\overline{Q+R}$
  2. $\overline{P+Q}$
  3. $\overline{P+R}$
  4. $\overline{P+Q+R}$
in Digital Logic by Veteran (105k points)
edited by | 3.8k views

The question is the realization of OR-AND(Product of Sum) using NOR gates.

 This is the realization of (P+Q)(Q+R) using NOR gates.

Give full explanation
if you understood the above logic then similarly for the second also we will realise using the Or-and realization .

so at the end, we will get  (pr+q) from first case and (pq+r) from the second case.

now this output will act as the input for the last NOR gate .

((pr+q) +(pq+r))' =which can be written as (r(p+1) +q(p+1))' ..

now , on simplifying this we will get (q+r)'

@Bharti goyal 

AND-OR(SOP) circuit can be made using NAND- NAND circuit.

OR-AND (POS) can be made using NOR-NOR circuit.



Self solved Boolean algebra method

@Bharti goyal  3rd line. you took R' common, then P' must be inside the bracket not R'


Try thisπŸ‘


Try these one too

1st line ??


4 Answers

+21 votes
Best answer
$​\text{ Level 1:}$
$(\overline{P + Q}) (\overline{Q + R}) (\overline{P + R}) (\overline{Q + R})$

$\text{ Level 2:}$
$\overline{(\overline{P + Q})+(\overline{Q + R})} = (P+Q)(Q+R)=PQ+PR+Q+QR$
$\overline{(\overline{P + R}) (\overline{Q + R})} = (P+R)(Q+R)=PQ+R+QR+PR$

$\text{ Level 3:}$
$\\\overline{PR+QR+PQ+Q+R} =\overline{Q+R}\\ \therefore \text{ Answer: Option A} ​$
by Active (4.2k points)
can you please give simplification of level 3.?
PR+QR+PQ+Q+R -->

Take Q common in Q and QP. We get Q(1+P) = Q

Similarly, R common in PR and QR. We get Q and P and the result.
we can simply replace nor nor ckt to or and ... it will make easy ckt
Good Explanation
${\color{Purple} {\implies \text{NOR - NOR Realization is equal to OR - AND  Realization.}}}$

${\color{Teal} {\implies \text{NAND - NAND Realization is equal to AND - OR  Realization.}}}$

So, we can easily solve and get the simplified expression $ = \overline{Q + R}$
+7 votes
[((P'Q') + (Q'R'))' + (P'R') + (Q'R'))']'

[(Q'(P' + R'))' + (R'(P' + Q'))']'

[(Q + PR + R + PQ)]'

[Q(1 + P) + R(1 + P)]'

[Q + R]'---------Answer.
by Boss (19.9k points)
+5 votes

Using De-Morgan's law: $\overline{\overline{(P+Q)}+\overline{(Q+R)}}=\overline{\overline{(P+Q)}}.\overline{\overline{(Q+R)}}$ and $\overline{\overline{(P+R)}+\overline{(Q+R)}}=\overline{\overline{(P+R)}}.\overline{\overline{(Q+R)}}$


Q + QR = Q and R + QR = R [absorption law]


Q + PQ = Q and R + PR = R

by Active (2.8k points)
edited by
Nicely explained :) tnx
–1 vote
answer - A

use de morgan's law
by Loyal (8.6k points)

Related questions

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
50,737 questions
57,321 answers
105,142 users