This is the format in 5.19 Convertthefollowingbinaryandhexadecimalnumberstooatin

Question

This is the format in 5.19

Convertthefollowingbinaryandhexadecimalnumberstooatingpointformat. Assume a binary format consisting of a sign bit (negative = 1), a base 2, 8-bit, excess-128 exponent, and 23 bits of mantissa, with the implied binary point to the right of the rst bit of the mantissa. t

1. Convert the following to the floating point representation using the format in 5.19 of your text: 12526588.125

2. Convert the following from the floating point representation to a decimal (base 10) representation using the format in 5.19 of your text: 10010110010010100011011010101011

please i need all the solutions.

Explanation / Answer

1)
Decimal representation:- 12526588.125

Sign bit = 0

exponent = 150 = 2^23

mantissa = 1.4932856559753418

5.1 format = 01001011001111110010001111111100

2)

Binary representation :-
10010110010010100011011010101011

sign bit = 1

exponent bit = 00101100 = 2^83

mantissa bits = 10010100011011010101011 = 1.5797933340072632

Therefore, by calculating we get , decimal representation = -1.633468E-25

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