## 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

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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

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

- Excess-3 codes are weighted and can be obtained by adding 3 to each decimal digit.
- Excess-3 code is non-weighted and self-complementary.
- 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

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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}

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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?

- It would increase the precision.
- Precision would remain unchanged, but the range would decrease.
- Precision would decrease, and range would increase.
- 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

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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

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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 * 2
^{10} - 1.0101010011 * 2
^{8} - 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

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