Consider the following two 7-bit floating-point representations based on the IEE
ID: 3596684 • Letter: C
Question
Consider the following two 7-bit floating-point representations based on the IEEE floating point format. Neither has a sign bit--they can only represent nonnegative numbers 1. Format A · There are k = 3 exponent bits. The exponent bias is 3. · There are n = 4 fraction bits. 2. Format B · There are k = 4 exponent bits. The exponent bias is 7. · There are n = 3 fraction bits. Below, you are given some bit patterns in Format A, and your task is to convert them to the closest value in Format B. If necessary, you should apply the round-to-even rounding rule. In addition, give the values of numbers given by the Format A and Format B bit patterns. Specify values as whole numbers or decimals. Please specify bit pattern for Format B within double quotation marks and without a space. (E.g.: "0111000") Finally to summarize the types expected for blanks--the columns titled "Value" expect decimal values and column titled "Bits" expects a bit pattern within quotes. (E.g.: 0111000 FormatA Bits 011 0000 101 1110 FormatB Bits 0111000 Value Value 1 010 1001 000 0001Explanation / Answer
Format A
101 1110
Exponent=5-3=2
Mantissa=0.5+0.25+0.125=0.875
Value=1.875*2^2=7.5
010 1001
Exponent=2-3=-1
Mantissa=0.5+0+0+0.0625=0.5625
Value=1.5625*2^(-1)=0.78125
110 1111
Exponent=6-3=3
Mantissa=0.5+0.25+0.125+0.0625=0.9375
Value=1.9375*2^3=15.5
000 0001
Exponent=0-3=-3
Mantissa=0+0+0+0.0625=0.0625
Value=1.0625*2^(-3)=0.1328125
Format B
101 1110 ==1010 000
Exponent=10-7=3
Mantissa=0
Value=1.0*2^3=8(Rounding to even)
010 1001 ==0000 000
Value=0(Rounded to even)
110 1111=1011 000
Exponent=11-7=4
Mantissa=0
Value=1.0*2^4=16(Rounded from 15.5)
000 0001=0000 000
Value=0 (Round to even)
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