61. If the two numbers are to be multiplied, the mantissa is multiplied and the exponents are added.
A. True
B. False
Answer: A
Let us consider two numbers X=M.2E and Y=N.2F
If we multiply both X and Y, we get X.Y=(M.N).2E+F
Thus if we multiply two numbers, the mantissa is multiplied and the exponents are added.
62. What is the smallest floating-point number that can be represented using a 32-bit word?
A. 3*10-38
B. 2*10-38
C. 0.2*10-38
D. 0.3*10-38
Answer: D
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.
Thus, the smallest floating-point number that can be represented using the 32-bit number is
(1/2)*2-127 = 0.3*10-38
Thus, the smallest floating-point number that can be represented using the 32-bit number is
(1-2-23)*2127 = 1.7*1038.
63. If 0<E<255, then which of the following statement is true about X?
B. Infinity
C. Mixed number
D. Zero
Answer: C
According to the IEEE 754 standard, for a 32-bit machine, a single-precision floating-point number is represented as X=(-1)s.2E-127(M).
From the above equation, we can interpret that,
If 0<E<255, then X=(-1)s.2E-127(1.M)=>X is a mixed number.
64. For a twos complement representation, the truncation error is _________
A. Always positive
B. Always negative
C. Zero
D. None of the mentioned
Answer: B
For a two’s complement representation, the truncation error is always negative and falls in the range
-(2-b-2-bm) ≤ Et ≤ 0.
65. Due to non-uniform resolution, the corresponding error in a floating-point representation is proportional to the number being quantized.
A. True
B. False
Answer: A
In floating-point representation, the mantissa is either rounded or truncated. Due to non-uniform resolution, the corresponding error in a floating-point representation is proportional to the number being quantized.
66. What is the binary equivalent of (-3/8)?
A. (10011)2
B. (0011)2
C. (1100)2
D. (1101)2
Answer: D
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 two’s complement of 0011=1101.
67. 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
Answer: B
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).
68. 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
Answer: C
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.
69. 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
Answer: B
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.
The largest floating-point number that can be represented using a 32-bit word is 1.7*1038
70. 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
Answer: D
According to the IEEE 754 standard, for a 32-bit machine, a 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.