# (Solved Homework): Practice. Consider the following two single precision bit patterns 1 011 11 110 1000 100 00000000000001 00 1 100

It’s language independt, just perform the addition.

Practice. Consider the following two single precision bit patterns 1 011 11 110 1000 100 00000000000001 00 1 100 000 11 11 11 110 0000000000000010 Perform binary addition of these 2 numbers following the algorithm for floating point addition given on Slides E20 & 21. Show all steps in your calculation

both s1 & s2 are 1

so both are -ve numbers

sum also will be a -ve number

first convert single precision numbers to deciamla numbers

1 01111110 1000100000000000000010

s1=1

exponent is biased here

01111110 equal to 126

bias is 127

now our exponent will be -1 ( exponent -bias)

mantissa when converted to binary( process is m1*2^-1+m2*2^-2………m23*2^-23) ,it is equal to 1.5312504

to convert all these into decimal format ,the formul is

-1^s m*2^exponent

now our first decimal number is -0.7656252

second number is 1 10000011 111111000000000000000000010

sign -1 (-ve)

10000011 means 131

real exponent is (131-127)   4

mantissa calculated with above formula -31.750003814

now we will calculate with algorithm

e1=-1

e2=4

e1-e2=5

shift smaller number(1st number through 5 places)

M1 will be00000100010000000000000000000

sum will be

1 0000000001000000000000010

one 1 is excess here now

increment exponent 10000100

now conver it into decimal

1 10000100 0000000010000000000010

now convert it into decimal

32.0315235

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