GATE CS Digital Logic questions

Consider an array multiplier for multiplying two $n$ bit numbers. If each gate in the circuit has a unit delay, the total delay of the multiplier is

Assuming all numbers are in $2’s$ complement representation, which of the following numbers is divisible by $11111011$?

Let $f(A,B) = A'+B$. Simplified expression for function $f(f(x+y, y), z)$ is

Consider the following multiplexer where $I0, I1, I2, I3$ are four data input lines selected by two address line combinations $A1A0=00,01,10,11$ respectively and $f$ is the output of the multiplexor. EN is the Enable input. The function $f(x,y,z)$ implemented by the above circuit is

Consider the following logic circuit whose inputs are functions $f_1, f_2, f_3$ and output is $f$ Given that $f_1(x,y,z) = \Sigma (0,1,3,5)$ $f_2(x,y,z) = \Sigma (6,7),$ and $f(x,y,z) = \Sigma (1,4,5).$ $f_3$ is

In $2's$ complement addition, overflow

Sign extension is a step in

The decimal value $0.25$

The $2's$ complement representation of the decimal value $-15$ is

Minimum sum of product expression for $f(w,x,y,z)$ shown in Karnaugh-map below

Consider the circuit given below with initial state $Q_0=1, Q_1=Q_2=0$. The state of the circuit is given by the value $4Q_2+2Q_1+Q_0$ Which one of the following is correct state sequence of the circuit?

Consider the circuit shown below. The output of a $2:1$ MUX is given by the function $(ac' + bc)$. Which of the following is true?

The $2's$ complement representation of (-539)10 in hexadecimal is

Consider the following circuit with initial state $Q_0 = Q_1 = 0$. The D Flip-flops are positive edged triggered and have set up times 20 nanosecond and hold times $0.$ Consider the following timing diagrams of X and C. The clock period of $C \geq 40$ nanosecond. Which one is the correct plot of Y?

Given the following karnaugh map, which one of the following represents the minimal Sum-Of-Products of the map?

Consider the values of $A = 2.0 \times 10^{30}, B = -2.0 \times 10^{30}, C = 1.0,$ and the sequence X:= A + B Y:= A + C X:= X + C Y:= Y + B executed on a computer where floating point numbers are represented with $32$ bits. The values for $X$ and $Y$ will be

The following arrangement of master-slave flip flops has the initial state of $P, Q$ as $0, 1$ (respectively). After three clock cycles the output state $P, Q$ is (respectively),

Which functions does NOT implement the Karnaugh map given below?

The simultaneous equations on the Boolean variables $x, y, z$ and $w$, $x + y + z = 1$ $xy = 0$ $xz + w = 1$ $xy + \bar{z}\bar{w} = 0$ have the following solution for $x, y, z$ and $w,$ respectively:

The number $43$ in $2's$ complement representation is