Question

Convert the following binary floating point number

100101.1001010101

using IEEE-756 single precision representation

Plz show work, thanks!

Answer 1

given binary floating point number : 100101.1001010101

i) spaces to move binary point so that it lands just after first 1 in the floating point number : 5
This gives us : 1.001011001010101
note: if we have to move left then it is positive else negative

ii) Add 127 to get exponent : 132
iii) convert exponent to binary : 10000100
iv) Adjust the Mantissa by removing the leading 1 from number we got in step 1
001011001010101

v) Result : 0 10000100 001011001010101
first 0 is sign bit : 0 means positive. positive since we moved left in step 1
next 8 bit is exponent
next 23 bit is mantissa