GATE 2020 IN – Question 18

Digital Electronics · Number systems and combinational logic: Number systems, multiplexer and demultiplexer, truth tables, minimization of Boolean functions, IC families (ECL, TTL, CMOS), CMOS logic gates, arithmetic circuits · 1 mark · Multiple choice

Let $f(A,B,C,D)=\sum m(0,1,2,6,8,9,10,11)+\sum d(3,7,14,15)$, where m denotes minterms and d don’t-cares. The minimal sum-of-products expression is

$A\bar B+CB$
$\bar B+C$
$\bar D+A$
$\bar A B+\bar C D$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (B) $\bar B+C$

Explanation

The eight-cell group with B = 0 uses minterms 0,1,2,8,9,10,11 and don’t-care 3, giving $\bar B$. A second eight-cell group with C = 1 uses 2,6,10,11 and don’t-cares 3,7,14,15, giving C. These groups cover every required 1 and no required 0. Hence $f=\bar B+C$, option B.

More Number systems and combinational logic: Number systems, multiplexer and demultiplexer, truth tables, minimization of Boolean functions, IC families (ECL, TTL, CMOS), CMOS logic gates, arithmetic circuits questions

GATE 2020 IN Q21 – Choose the Boolean expression represented by the shaded Venn regions in the figure.
GATE 2020 IN Q22 – For the shown 4:1 multiplexer with select bits S 1 (MSB) and S 0 (LSB), the output O is
GATE 2025 IN Q17 – The minimized Boolean expression Y(P,Q,R) implemented by the shown multiplexer circuit is
GATE 2025 IN Q18 – The 4-bit signed two’s-complement result of (5) 10+(5) 10 is
GATE 2025 IN Q29 – A Boolean function is X= A B+ A C. The reduced form of X is
GATE 2024 IN Q16 – The simplified form of the Boolean function F=(A+ A B)+ A(A+ B)C is

All Number systems and combinational logic: Number systems, multiplexer and demultiplexer, truth tables, minimization of Boolean functions, IC families (ECL, TTL, CMOS), CMOS logic gates, arithmetic circuits questions →