Digital Logic

 Question 1
Consider the IEEE-754 single precision floating point numbers P=0xC1800000 and Q=0x3F5C2EF4.
Which one of the following corresponds to the product of these numbers (i.e., P x Q), represented in the IEEE-754 single precision format?
 A 0x404C2EF4 B 0x405C2EF4 C 0xC15C2EF4 D 0xC14C2EF4
GATE CSE 2023      Number System
Question 1 Explanation:
 Question 2
A Boolean digital circuit is composed using two 4-input multiplexers (M1 and M2) and one 2-input multiplexer (M3) as shown in the figure. X0-X7 are the inputs of the multiplexers M1 and M2 and could be connected to either 0 or 1. The select lines of the multiplexers are connected to Boolean variables A, B and C as shown.

Which one of the following set of values of (X0, X1, X2, X3, X4, X5, X6, X7) will realise the Boolean function $\bar{A}+\bar{A}\cdot \bar{C}+A\cdot \bar{B}\cdot C$ ?
 A (1, 1, 0, 0, 1, 1, 1, 0) B (1, 1, 0, 0, 1, 1, 0, 1) C (1, 1, 0, 1, 1, 1, 0, 0) D (0, 0, 1, 1, 0, 1, 1, 1)
GATE CSE 2023      Combinational Circuit
Question 2 Explanation:
 Question 3
Consider a sequential digital circuit consisting of T flip-flops and D flip-flops as shown in the figure. CLKIN is the clock input to the circuit. At the beginning, Q1, Q2 and Q3 have values 0, 1 and 1, respectively.

Which one of the given values of (Q1, Q2, Q3) can NEVER be obtained with this digital circuit?
 A (0, 0, 1) B (1, 0, 0) C (1, 0, 1) D (1, 1, 1)
GATE CSE 2023      Sequential Circuit
Question 3 Explanation:
 Question 4
A particular number is written as 132 in radix-4 representation. The same number in radix-5 representation is _____.
 A 158 B 118 C 110 D 98
GATE CSE 2023      Number System
Question 4 Explanation:
 Question 5
The output of a 2-input multiplexer is connected back to one of its inputs as shown in the figure.

Match the functional equivalence of this circuit to one of the following options.
 A D Flip-flop B D Latch C Half-adder D Demultiplexer
GATE CSE 2023      Combinational Circuit
Question 5 Explanation:
 Question 6
Consider three floating point numbers A, B and C stored in registers $R_A$, $R_B$ and $R_C$, respectively as per IEEE-754 single precision floating point format. The 32-bit content stored in these registers (in hexadecimal form) are as follows.

$R_A=0xC1400000$
$R_B=0x42100000$
$R_C=0x41400000$

Which one of the following is FALSE?
 A $A+C=0$ B $C=A+B$ C $B=3C$ D $(B-C) \gt 0$
GATE CSE 2022      Number System
Question 6 Explanation:
 Question 7
Let R1 and R2 be two 4-bit registers that store numbers in 2's complement form. For the operation R1+R2, which one of the following values of R1 and R2 gives an arithmetic overflow?
 A R1 = 1011 and R2 = 1110 B R1 = 1100 and R2 = 1010 C R1 = 0011 and R2 = 0100 D R1 = 1001 and R2 = 1111
GATE CSE 2022      Number System
Question 7 Explanation:
 Question 8
Consider a Boolean function $f(w,x,y,z)$ such that

$\begin{array}{lll} f(w,0,0,z) & = & 1 \\ f(1,x,1,z) & =& x+z \\ f(w,1,y,z) & = & wz +y \end{array}$

The number of literals in the minimal sum-of-products expression of $f$ is ________
 A 4 B 6 C 8 D 9
GATE CSE 2021 SET-2      Boolean Algebra
Question 8 Explanation:
 Question 9
If the numerical value of a 2-byte unsigned integer on a little endian computer is 255 more than that on a big endian computer, which of the following choices represent(s) the unsigned integer on a little endian computer?
[MSQ]
 A 0x6665 B 0x0001 C 0x4243 D 0x0100
GATE CSE 2021 SET-2      Number System
Question 9 Explanation:
 Question 10
If $x$ and $y$ are two decimal digits and $(0.1101)_2 = (0.8xy5)_{10}$, the decimal value of $x+y$ is ___________
 A 3 B 6 C 8 D 4
GATE CSE 2021 SET-2      Number System
Question 10 Explanation:

There are 10 questions to complete.

13 thoughts on “Digital Logic”

1. Sir, Please mention the a,b,c value of question 2.

• Hi Ashutosh,
Here, value of a,b,c are not required. You can write the truth table based on above circuit. Then find the answer based on truth table. See the solution provided.

2. Question 5, Please update the answer from 4 minimum gate to 3 minimum gate.

• Hi Ashutosh,
Thank you for your suggestion. We have updated the answer from 4 to 3.

3. Q13 answer will be B…
Update it

• Thank You akki yadav, We have updated the answer suggested by you.

4. Update Question No. 46. The options should be Q1Q0 instead of Q0Q1

5. Update Q56 as B instead of C

• Thank You Sowmya Sri,