Problem 2 (14 points. Suggested time: 10 mins) and 1 in binary normalized Part a

Question

Problem 2 (14 points. Suggested time: 10 mins) and 1 in binary normalized Part a (6 points): Express the two floating point numbers 2 form (3 points) 21 in binary normalized form is: (3 points) in binary normalized form is: Part b (4 points): As you know IEEE floating point standard has a 32-bit representation and a 64-bit representation. (2 points) What is the bias used in the 32-bit representation? (a points) What is the minimum gap between two representable subnormal numbers in the 32-bit representation? Part e (4 points): In this problem, we assume that IEEE decided to add a new 10-bit representation, with its main characteristics consistent with the other two representations. In this 10-bit representation, the value 33/256 is represented exactly as ooo1100001. Your job: decide the number of bits needed for the exponent and for the fraction. (2 points) Number of bits needed for exponent: (a points) Number of bits needed for fraction:

Explanation / Answer

General Information:

1 bit sign, 8 bit exponent, 23 bit mantissa

1 bit sign, 11 bit exponent, 52 bit mantissa

Part-A

1)2 15/16- the decimal value of this digit is 2.93

The binary floating value is 10.1110111000

The normalized binary form

1.01110111000(2)*21 (The exponent here is 1)

2)1/8- The decimal value of this digit is 0.125

The binary form is 0.001

Positive number is present before normalization

Normalize the binary representation of the number, shifting the decimal mark to 3 position

1(2)*2-3 (The exponent here is -3)

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