## NPTEL Digital System Design Week 1 Assignment Answers 2024

1. What is the hexadecimal equivalent of (101010101)2

- (157)16
- (155)16
- (1D6)16
- (196)16

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2. Convert (1ABC)1616Â into its equivalent octal representation.

- (15274)8
- (25274)8
- (25272)8
- (15272)8

Answer :-

3. Which of the following is equivalent to (1764)88.

1. (999)1010+(11)1010

2. (10000000000)-22(1100)22

3. (3E8)1616+(C)1616

4. (2114)88-(130)8

- Only 1
- Only 2 and 3
- Only 3 and 4
- Only 2, 3, and 4

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4. What is the decimal equivalent of the binary number 0.111011?

- 0.46875
- 0.484375
- 0.984375
- 0.921875

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5. Consider these two unsigned binary numbers (11111011)2Â and (11111010)2

Â . what is their addition?

- 111110101
- 111111110
- 101111101
- 111001110

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6. The range of values that can be represented by 10 bit in 2â€™s complement form is

- -512 to +512
- -512 to +511
- -256 to +256
- -256 to +255

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7. What is the 2â€™s complement of (19)1010Â in 8-bit format?

- 11101101
- 11101110
- 11110001
- 11101010

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8. In 16-bit 2â€™s complement representation, the decimal number -28 is

- 1111 1111 0001 1100
- 1111 1111 1110 0100
- 1000 0000 0000 1011
- 1000 0000 0010 1010

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9. The greatest negative number that can be stored in a 9-bit register using 2â€™s complement arithmetic

- -511
- -512
- -255
- -256

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10. What is the binary representation of 0.4 with a precision of 6 bits?

- 0.110011
- 0.011
- 0.011001
- 0.010011

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11. What is the addition of 11101111 (binary 2â€™s complement) with 00010111 (binary 2â€™s complement)?

- -40
- 6
- 262
- -21

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12. What is the number of 1s in the 2s’ complement binary representation of -42, considering an 8-bit binary representation?”

- 2
- 3
- 4
- 5

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13. Why does 1â€™s complement system in 8 bits have a different range than 2â€™s complement system in 8 bits?

- 1â€™s complement uses a sign bit, and 2â€™s complement does not
- 2â€™s complement has two representations for 0
- 1â€™s complement has two representations for 127
- 1â€™s complement has two representations for 0
- Both 1â€™s complement and 2â€™s complement have the same range

Answer :-

14. The minimum decimal equivalent of the number (67) is.

- 19
- 67
- 55
- 31

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