olution Floating point representation: It is defined as the representation of floating numbers. It includes sign bit, exponent, and mantissa bits. Based on precision it has 2 types. 1. For IEEE 754 single-precision floating-point numbers, what is the exponent of a denormalized floating-point number in decimal? Solution: In IEEE 754 single-precision, exponent bits are 8. Therefore exponent = 2 ^(n-1) -1 = 2^(8-1) -1 = 127 OPTION D 2. For IEEE 754 single-precision floating-point numbers, how many bits for mantissa? Solution: In IEEE 754 single-precision, there are 23 bits for mantissa. sign = 1 bit exponent = 8 bits mantissa = 23 bits 3. For IEEE 754 single-precision floating-point numbers, which of the following is an example of NAN? Solution: In IEEE 754 single-precision, NAN is a special value where all exponents bits are 1's and the mantissa is non zero. a. 1 111 1 111 0000 0000 1101 0000 0000 0000 Exponent is not all 1's. Not a NAN b. 0 111 1 111 1000 0000 1101 0000 0000 0000 Exponent is all 1's and the mantissa is non zero. IT IS A NAN. c. 0 111 1 111 1000 0000 0000 0000 0000 0000 Exponent is all 1's and mantissa is zero. IT IS NOT NAN. d. 1 111 1 111 0000 0000 0000 0000 0000 0000 Exponents is not all 1's. Not a NAN ANSWER: OPTION B
Floating point representation:
It is defined as the representation of floating numbers. It includes sign bit, exponent, and mantissa bits. Based on precision it has 2 types.
1. For IEEE 754 single-precision floating-point numbers, what is the exponent of a denormalized floating-point number in decimal?
Solution:
In IEEE 754 single-precision, exponent bits are 8.
Therefore exponent = 2 ^(n-1) -1 = 2^(8-1) -1 = 127
OPTION D
2. For IEEE 754 single-precision floating-point numbers, how many bits for mantissa?
Solution:
In IEEE 754 single-precision, there are 23 bits for mantissa.
sign = 1 bit
exponent = 8 bits
mantissa = 23 bits
3. For IEEE 754 single-precision floating-point numbers, which of the following is an example of NAN?
Solution:
In IEEE 754 single-precision, NAN is a special value where all exponents bits are 1's and the mantissa is non zero.
a. 1 111 1 111 0000 0000 1101 0000 0000 0000
Exponent is not all 1's. Not a NAN
b. 0 111 1 111 1000 0000 1101 0000 0000 0000
Exponent is all 1's and the mantissa is non zero.
IT IS A NAN.
c. 0 111 1 111 1000 0000 0000 0000 0000 0000
Exponent is all 1's and mantissa is zero.
IT IS NOT NAN.
d. 1 111 1 111 0000 0000 0000 0000 0000 0000
Exponents is not all 1's. Not a NAN
ANSWER: OPTION B
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