List of top Computer Science and IT Engineering Questions on Digital Logic asked in GATE CS

Consider the digital circuit shown below with two input lines A and B, two select
lines S0 and S1, and an output line Y. The blocks Q and M represent active high
2:4 decoder and 4-to-1 multiplexer, respectively. Out of 16 possible input
combinations, the number of combinations that produce Y=1 is ____________.
(answer in integer)
Note: One input combination is an instance of [A B S1 S0].

Consider the following 4-variable Boolean function
𝐹(𝐴, 𝐵, 𝐶, 𝐷) = Σ𝑚(0, 1, 2, 3, 8, 9, 10, 11)
Consider 𝐴 as MSB, 𝐷 as LSB. Which one of the following options represents the
minimal sum of products form for the above function?
Note: + is OR operation, . is AND operation, ′ is NOT operation

Which one of the following options is not a property of Boolean Algebra?
Note: + is OR operation, . is AND operation, and ′ is NOT operation

Consider a Boolean function F with the following minterm expression:
𝐹(𝑃, 𝑄, 𝑅, 𝑆) = ∑𝑚 (1, 2, 3, 4, 5, 7, 10, 12, 13, 14)
Which of the following options is/are the minimal sum-of-products expression(s)
of F ?

Consider a 2-bit saturating up/down counter that performs the saturating up count
when the input P is 0, and the saturating down count when P is 1. The Next State
table of the counter is as shown. The counter is built as a synchronous sequential
circuit using D flip-flops.
Input
Current
State
Next
State
𝑃
𝑄1
𝑄0
𝑄1
+
𝑄0
+
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
1
1
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
1
1
1
0
Which one of the following options corresponds to the expressions for the inputs of
the D flip-flops, 𝐷1 and 𝐷0?

Consider the following Boolean expression of a function F :
𝐹(𝑃, 𝑄) = (𝑃̅ + 𝑄) ⊕(𝑃̅𝑄)
Which of the following expressions is/are equivalent to F ?