# NPTEL Digital System Design Week 2 Assignment Answers 2024

## NPTEL Digital System Design Week 2 Assignment Answers 2024

1. Consider three numbers represented in standard single-precision format: A, B, and C. Which of the given relations is true?
A = 0x41400000
B = 0xc1400000
C = 0xc2040000

• A + B < C
• A + B = 0
• A + B = C
• A + C = B
`Answer :- For Answer Click Here `

2. According to 64-bit IEEE754 single precision, what is the number of bits for sign, exponent, and mantissa, respectively?

• 1, 8, 55
• 2, 10, 52
• 2, 7, 55
• 1, 11, 52
• 2, 13, 51
`Answer :- For Answer Click Here `

3. Which of the following statements about the Excess-3 code are true?

1.  Excess-3 codes are weighted and can be obtained by adding 3 to each decimal digit.
2.  Excess-3 code is non-weighted and self-complementary.
3.  The codes 0000 and 1111 are not used for any digit in Excess-3 codes, which is an advantage for memory organization as these codes can cause faults in the transmission line.
• Only 1
• Only 1 and 2
• Only 2 and 3
• 1,2 and 3
`Answer :- For Answer Click Here `

4. Which of the following codes is used to reduce error due to ambiguity in reading a binary optical encoder?

• Octal code
• BCD code
• Excess 3 code
• Gray code
`Answer :- `

5. Two 4-bit numbers, r1, and r2, that store numbers in 2’s complement form. If we do an addition operation as r1+r2, which out of the following combinations of r1 and r2 would result in arithmetic overflow?

• r1 = 1110 and r2 = 1100
• r1 = 1111 and r2 =1001
• r1 = 1011 and r2 = 1010
• r1 = 0011 and r2 = 0011
`Answer :- `

6. Consider the following 32-bit (single precision) IEEE-754 format binary number – 00111110011011010000000000000000; which of the following values is closest to this number?

• 2.00 x 10-1
• 2.25 x 10-1
• 2.50 x 10-1
• 2.75 x 10-1
`Answer :- For Answer Click Here `

7. Which of the following points are valid if we make the exponent field 10 bits and the mantissa part 21 bits in IEEE 754 Single Precision Floating point format?

1. It would increase the precision.
2. Precision would remain unchanged, but the range would decrease.
3. Precision would decrease, and range would increase.
4. The range would decrease
• Only 1
• Only 2 and 4
• Only 1 and 4
• Only 3
`Answer :- `

8. Convert the decimal number “-23296.0” into a 32-bit IEEE 754 floating point representation

• 0xc6b600000
• xcba600000
• xa69c00000
• xac400000
`Answer :- `

9. The maximum number which can be represented by 4 bit BCD code is

• 8
• 10
• 91
• 1
`Answer :- `

10. The IEEE 754 32-bit representation of -4.15625 is?

• 0xc0465000
• 01000000100001010000000000000000
• 0xc0850000
• 10000000100001010000000000000000
`Answer :- For Answer Click Here `

11. Convert the given Excess 3 code (0101 1001) into BCD format.

• 0010 0110
• 0110 0110
• 0110 0000
• 1001 0011
`Answer :- `

12. Consider three 32 bit numbers, R1, R2, and R3, that store values in IEEE-754 single precision floating point format. R1 and R2 contain the values, 0xc1c80000 and 0x41200000 respectively. If R3 = R1R2 . What is the value of R3?

• 0x41c80000
• 0x40200000
• 0xc0200000
• 0xc1200000
`Answer :- For Answer Click Here `

13. Consider an encoding called Excess-3 Gray code, which is the same as the gray code of the decimal plus 3.
Excess 3 Gray Code (x) = Gray Code (x+3).
For example, Excess-3 Gray code of 4 will be Gray Code of (4+3=7), which is 0100

Now,what is the Excess-3 Gray Code of 2187?

• 0011 0001 1100 0100
• 0111 0110 1110 1111
• 0011 0001 1110 1111
• 0111 0110 1100 0100
`Answer :- `

14. Convert the binary fractional number 00101010100.11 in normalized form

• 101010100.11
• 0.010101010011 * 210
• 1.0101010011 * 28
• 101010100.11 * 2-2
`Answer :- `

15. When two BCD numbers XXXX XXXX XXXX and YYYY YYYY YYYY are added, the following results are obtained. Which one is the correct result of addition?

• 1010 1000 0011 1001
• 0001 0101 1000 0011
• 0010 1101 0010 0101
• 0101 1101 0001 1101
`Answer :- For Answer Click Here `