1. What decimal number would the IEEE 754 single precision floating point number

Question

1. What decimal number would the IEEE 754 single precision floating point number 0xC3F2B800 (this is in hex) be? Write your final answer in scientific notation as m x 10 p where p is an integer.

PLEASE SHOW DETAILED SOLUTION.

2. Add 3.19 ten x 10 9 to 6.28 ten x 10 8, assuming the following two different ways:

a)  you have only three significant digits, first with guard (2 digits) and round digits.

b) you have only three significant digits without guard and rounding.

PLEASE SHOW DETAILED SOLUTION.

Explanation / Answer

1) C3F2B800 in binary is

1100 0011 1111 0010 1011 1000 0000 0000

1   10000111   111 0010 1011 1000 0000 0000

First bit is Sign bit = 1 which means '-'ve number

Next 8 bits are for Biased Exponent, BE

BE= (10000111)2 = (135)10

BE= Actual Exponent + Bias where Bias=127

=> 135=Actual Exponent+127

=> Actual Exponent = 135-127 =8

Next, 23 bits are for mantissa

111 0010 1011 1000 0000 0000

= 2-1 + 2-2 + 2-3 + 2-6 + 2-8 + 2-10 + 2-11 + 2-12

= 0.5 + 0.25 + 0.125 + 0.015625 + 0.00390625 + 0.0009765625 + 0.00048828125 + 0.000244140625

= 0.896240234375

Number is (-1)S 1.M * 2E

Hence. the number is - 1.896240234375 * 28 = 485.4375 = 4.854375 * 102

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