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Mips architecture 1. (20 points) Assuming the IEEE 754 single precision format i

ID: 3594133 • Letter: M

Question

Mips architecture

1. (20 points) Assuming the IEEE 754 single precision format i. Decimal representation: a ii. Normalized binary representation: b × 2c ii Exponent bits: d (insert ' symbol every 4 bits) iv. Fraction bits: e (insert '' symbol every 4 bits) v. Hexadecimal representation: f (a) (10 points) Find the value of b, c, d, e, and f when you convert the decimal number a= 63.25 to the hexadecimal representation. (b) (10 points) Find the value of e, d, c, b, and a when you convert the hexadecimal number f = 0x2e92c3bf to the decimal representation.

Explanation / Answer

Solution:

a)

First, we will convert 63.25 into binary representation

111111.01

let's change it into the normalized form

1.11111101 * 2^5

exponent= bias + biased exponent= 127 + 5= 132

Now,

d= 1000|0100

e= 1111|1101|0000|0000|0000|000

f= 0x427D0000

b)

0x2e92c3bf

in binary 0010 1110 1001 0010 1100 0011 1011 1111

d= 0101|1101, in decimal 93

e= 0010|0101|1000|0111|0111|111

Actual exponent= 127-93= 34

in binary 1.00100101100001110111111 * 2^34

= 100100101100001110111111 * 2^9

= 4924603904

Please upvote and raise your doubts within the comment.

Sign Exponent Mantissa 0 1000|0100 1111|1101|0000|0000|0000|000