GATE CS Digital Logic questions

The minimum number of $\text{JK}$ flip-flops required to construct a synchronous counter with the count sequence $(0, 0, 1, 1, 2, 2, 3, 3, 0, 0, \ldots)$ is _______.

Given the function $F = P' +QR$, where $F$ is a function in three Boolean variables $P, Q$ and $R$ and $P'=!P$, consider the following statements. $(S1) F = \sum(4, 5, 6)$ $(S2) F = \sum(0, 1, 2, 3, 7)$ $(S3) F = \Pi (4, 5, 6)$ $(S4) F = \Pi (0, 1, 2, 3, 7)$ Which of the following is true?

The total number of prime implicants of the function $f(w, x, y, z) = \sum (0, 2, 4, 5, 6, 10)$ is __________

Consider the equation $(43)_x = (y3)_8$ where $x$ and $y$ are unknown. The number of possible solutions is _____

Consider the $4\text{-to-1}$ multiplexer with two select lines $S_1$ and $S_0$ given below The minimal sum-of-products form of the Boolean expression for the output $F$ of the multiplexer is

The base (or radix) of the number system such that the following equation holds is____________. $\frac{312}{20} = 13.1$

Consider the following Boolean expression for F: $F(P,Q,R,S)= PQ + \bar{P}QR + \bar{P}Q\bar{R}S$ The minimal sum$-$of$-$products form of $F$ is

The value of a $\text{float}$ type variable is represented using the single-precision $\text{32-bit}$ floating point format of $\text{IEEE-754}$ standard that uses $1$ $\text{bit}$ for sign, $\text{8 bits}$ for biased exponent and $\text{23 bits}$ for the mantissa. A $\text{float}$ type variable $X$ is assigned the decimal value of …

Let $k=2^n$. A circuit is built by giving the output of an $n$-bit binary counter as input to an $n\text{-to-}2^n$ bit decoder. This circuit is equivalent to a

Consider the equation $(123)_5=(x8)_y$ with $x$ and $y$ as unknown. The number of possible solutions is _____ .

The dual of a Boolean function $F(x_1,x_2,\dots,x_n,+, .,')$, written as $F^D$ is the same expression as that of $F$ with $+$ and $⋅$ swapped. $F$ is said to be self-dual if $F = F^D$. The number of self-dual functions with $n$ Boolean variables is

Let $\oplus$ denote the exclusive OR (XOR) operation. Let '$1$' and '$0$' denote the binary constants. Consider the following Boolean expression for $F$ over two variables $P$ and $Q$: $$F(P,Q)=\left( \left(1 \oplus P \right) \oplus \left( P \oplus Q \right )\right ) \oplus \left(\left(P \oplus Q\right) \oplus \left(Q \oplus 0\right)\right)$$ The …

The above synchronous sequential circuit built using JK flip-flops is initialized with $Q_2Q_1Q_0 = 000$. The state sequence for this circuit for the next $3$ clock cycles is

Consider the following combinational function block involving four Boolean variables $x,\:y,\:a,\:b$ where $x,\:a,\:b$ are inputs and $y$ is the output. f(x, a, b, y) { if(x is 1) y = a; else y = b; } Which one of the following digital logic blocks is the most suitable for implementing this function?

Consider the following minterm expression for $F$: $$F(P,Q,R,S) = \sum 0,2,5,7,8,10,13,15$$ The minterms $2$, $7$, $8$ and $13$ are 'do not care' terms. The minimal sum-of-products form for $F$ is

A RAM chip has a capacity of 1024 words of 8 bits each (1K × 8). The number of 2 × 4 decoders with enable line needed to construct a 16K × 16 RAM from 1K × 8 RAM is

Which one of the following expressions does NOT represent exclusive NOR of $x$ and $y$?

In the following truth table, $V = 1$ if and only if the input is valid. …

The smallest integer that can be represented by an $8\text{-bit}$ number in $2's$ complement form is

What is the minimal form of the Karnaugh map shown below? Assume that $X$ denotes a don’t care term