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

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) 2^{E}

b) M.2^{E}(1/2<M<1 )

c) 2M.2^{E}(1/2<M<1 )

d) None of the mentioned

View Answer

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 2

^{E}, where the exponent E is either a negative or positive integer. Hence a number X is represented as X= M.2

^{E}(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

Explanation: We can represent the numbers in binary float point as

5=0.101000(2

^{011})

3/8=0.110000(2

^{101})=0.000011(2

^{011})

=>5+3/8=(0.101000+0.000011)(2

^{011})=(0.101011)(2

^{011})

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*10^{38}

b) 1.7*10^{38}

c) 0.2*10^{38}

d) 0.3*10^{38}

View Answer

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.

a) Not a number

b) Infinity

c) Defined

d) Zero

View Answer

Explanation: According to the IEEE 754 standard, for a 32-bit machine, single precision floating point number is represented as X=(-1)

^{s}.2

^{E-127}(M).

From the above equation we can interpret that,

If E=0 and M=0, then the value of X is 0.

6. The truncation error for the sign magnitude representation is symmetric about zero.

a) True

b) False

View Answer

Explanation: The truncation error for the sign magnitude representation is symmetric about zero and falls in the range

-(2

^{-b}-2

^{-bm}) ≤ E

_{t}≤ (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

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})].

8. What is the 2’s complement of (1100)_{2}?

a) (0100)_{2}

b) (0011)_{2}

c) (0111)_{2}

d) (1100)_{2}

View Answer

Explanation: 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}.

_{-A}is called as:

a) LSB

b) Total value

c) MSB

d) None of the mentioned

View Answer

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.

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

Explanation: According to the IEEE 754 standard, for a 32-bit machine, single precision floating point number is represented as X=(-1)

^{s}.2

^{E-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.**

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