Digital Signal Processing Questions and Answers – Representation of Numbers – 2

This set of Digital Signal Processing Interview Questions & Answers focuses on “Representation of Numbers”.

1. What is the binary equivalent of (-3/8)?
a) (10011)2
b) (0011)2
c) (1100)2
d) (1101)2
View Answer

Answer: d
Explanation: The number (-3/8) is stored in the computer as the 2’s complement of (3/8)
We know that the binary equivalent of (3/8)=0011
Thus the twos complement of 0011=1101.

2. Which of the following is the correct representation of a floating point number X?
a) 2E
b) M.2E(1/2<M<1)
c) 2M.2E(1/2<M<1)
d) None of the mentioned
View Answer

Answer: b
Explanation: The binary floating point representation commonly used in practice, consists of a mantissa M, which is the fractional part of the number and falls in the range 1/2<M<1, multiplied by the exponential factor 2E, where the exponent E is either a negative or positive integer. Hence a number X is represented as X= M.2E(1/2<M<1).

3. What is the mantissa and exponent respectively obtained when we add 5 and 3/8 in binary float point representation?
a) 0.101010,011
b) 0.101000,011
c) 0.101011,011
d) 0.101011,101
View Answer

Answer: c
Explanation: We can represent the numbers in binary float point as
5=0.101000(2011)
3/8=0.110000(2101)=0.000011(2011)
=>5+3/8=(0.101000+0.000011)(2011)=(0.101011)(2011)
Therefore mantissa=0.101011 and exponent=011.

4. What is the largest floating point number that can be represented using a 32-bit word?
a) 3*1038
b) 1.7*1038
c) 0.2*1038
d) 0.3*1038
View Answer

Answer: b
Explanation: Let the mantissa be represented by 23 bits plus a sign bit and let the exponent be represented by 7 bits plus a sign bit.
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5. If E=0 and M=0, then which of the following statement is true about X?
a) Not a number
b) Infinity
c) Defined
d) Zero
View Answer

Answer: d
Explanation: According to the IEEE 754 standard, for a 32-bit machine, single precision floating point number is represented as X=(-1)s.2E-127(M).
From the above equation we can interpret that,
If E=0 and M=0, then the value of X is 0.
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6. The truncation error for the sign magnitude representation is symmetric about zero.
a) True
b) False
View Answer

Answer: a
Explanation: The truncation error for the sign magnitude representation is symmetric about zero and falls in the range
-(2-b-2-bm) ≤ Et ≤ (2-b-2-bm).

7. What is the range of round-off error for a foxed point representation?
a) [-0.5(2-b+2-bm), 0.5(2-b+2-bm)]
b) [0, (2-b+2-bm)]
c) [0, (2-b-2-bm)]
d) [-0.5(2-b-2-bm), 0.5(2-b-2-bm-bm)]
View Answer

Answer: d
Explanation: The round-off error is independent of the type of fixed point representation. The maximum error that can be introduced through rounding is 0.5(2-b+2-bm) and this can be either positive or negative, depending on the value of x. Therefore, the round-off error is symmetric about zero and falls in the range
[-0.5(2-b-2-bm), 0.5(2-b-2-bm-bm)].
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8. What is the 2’s complement of (1100)2?
a) (0100)2
b) (0011)2
c) (0111)2
d) (1100)2
View Answer

Answer: a
Explanation: The ones complement of (1100)2 is (0011)2. Thus the two complement of this number is obtained as (0011)2+(0001)2=(0100)2.

9. The binary digit b-A is called as ______________
a) LSB
b) Total value
c) MSB
d) None of the mentioned
View Answer

Answer: c
Explanation: Since the binary digit b-A is the first bit in the representation of the real number, it is called as the most significant bit(MSB) of the number.
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10. If E=255 and M≠0, then which of the following statement is true about X?
a) Not a number
b) Infinity
c) Defined
d) Zero
View Answer

Answer: a
Explanation: According to the IEEE 754 standard, for a 32-bit machine, single precision floating point number is represented as X=(-1)s.2E-127(M).
From the above equation we can interpret that,
If E=255 and M≠0, then X is not a number.

Sanfoundry Global Education & Learning Series – Digital Signal Processing.

To practice all areas of Digital Signal Processing for interviews, here is complete set of 1000+ Multiple Choice Questions and Answers.

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Manish Bhojasia - Founder & CTO at Sanfoundry
Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He lives in Bangalore, and focuses on development of Linux Kernel, SAN Technologies, Advanced C, Data Structures & Alogrithms. Stay connected with him at LinkedIn.

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