# Digital Logic

 Question 1
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 1 Explanation:
 Question 2
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 2 Explanation:
 Question 3
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 3 Explanation:
 Question 4
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 4 Explanation:
 Question 5
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 5 Explanation:
 Question 6
Which one of the following circuits implements the Boolean function given below?

$f(x,y,z) = m_0+m_1+m_3+m_4+m_5+m_6$

where $m_i$ is the $i^{th}$ minterm.

 A A B B C C D D
GATE CSE 2021 SET-2      Combinational Circuit
Question 6 Explanation:
 Question 7
The format of the single-precision floating point representation of a real number as per the IEEE 754 standard is as follows:

$\begin{array}{|c|c|c|} \hline \text{sign} & \text{exponent} & \text{mantissa} \\ \hline \end{array}$

Which one of the following choices is correct with respect to the smallest normalized positive number represented using the standard?
 A exponent = 00000000 and mantissa = 0000000000000000000000000 B exponent = 00000000 and mantissa = 0000000000000000000000001 C exponent = 00000001 and mantissa = 0000000000000000000000000 D exponent = 00000001 and mantissa = 0000000000000000000000001
GATE CSE 2021 SET-2      Number System
Question 7 Explanation:
 Question 8
Consider the following Boolean expression.

$F=(X+Y+Z)(\overline X +Y)(\overline Y +Z)$

Which of the following Boolean expressions is/are equivalent to $\overline F$ (complement of $F$)?
[MSQ]
 A $(\overline X +\overline Y +\overline Z)(X+\overline Y)(Y+\overline Z)$ B $X\overline Y + \overline Z$ C $(X+\overline Z)(\overline Y +\overline Z)$ D $X\overline Y +Y\overline Z + \bar X \bar Y \bar Z$
GATE CSE 2021 SET-1      Boolean Algebra
Question 8 Explanation:
 Question 9
Consider a 3-bit counter, designed using T flip-flops, as shown below:

Assuming the initial state of the counter given by PQR as 000, what are the next three states?
 A 011,101,000 B 001,010,111 C 011,101,111 D 001,010,000
GATE CSE 2021 SET-1      Sequential Circuit
Question 9 Explanation:
 Question 10
Consider the following representation of a number in IEEE 754 single-precision floating point format with a bias of 127.

S:1
E:10000001
F:11110000000000000000000

Here, S,E and F denote the sign, exponent, and fraction components of the floating point representation.

The decimal value corresponding to the above representation (rounded to 2 decimal places) is ____________.
 A -7.75 B 7.75 C -3.825 D 3.825
GATE CSE 2021 SET-1      Number System
Question 10 Explanation:

There are 10 questions to complete.

### 12 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,