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# 16 bit floating point format

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Use the 16 bit floating point format to perform the following:

a) Convert ED80 from fpx to decimal.
b) Convert 1.745 * 10-3 from decimal to fpx.
c) Add two fpx numbers (7B80 + 7300).
d) Subtract two fpx numbers (7700 - 7CF0).
e) Multiply two fpx numbers (7500 * A70A).

All above numbers are fp (floating point) in hexadecimal, except for 1b, which is given in decimal.

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https://brainmass.com/computer-science/algorithms/16-bit-floating-point-format-235233

#### Solution Preview

Since nothing is mentioned about the 16 bit floating point format in the question, this solution considers 16 bit Half Precision floating point format as mentioned at http://en.wikipedia.org/wiki/Half_precision .

Bits layout in 16 bit (Half Precision) floating point format is as follows.

(1 Sign bit, 5 Exponent bits, 10 Fraction/Significand bits)

Exponent bias (b) = 15

In the response below, suffixes H and B are used to indicate hexadecimal and binary values respectively.

a) Convert ED80 from fpx to decimal

(ED80)H = (1110 1101 1000 0000)B

Sign bit (S) = 1
Exponent bits (e) = (11011)B = 27
Fraction bits (f) = (01 1000 0000)B

Equivalent decimal number = (-1)^S * 2^(e-b) * (1.f)B
= (-1)^1 * 2^(27-15) * (1.0110000000)B
= - 2^12 * (1.0110000000)B
= - (1011000000000)B
= - (4096+1024+512)
= - 5632 or -5632.00

b) Convert 1.745 * 10^(-3) from ...

#### Solution Summary

Since nothing is mentioned about the 16 bit floating point format in the question, this solution considers 16 bit Half Precision floating point format as mentioned at http://en.wikipedia.org/wiki/Half_precision .

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