Floating Point Arithmetic — Changing Decimal to FP: Computer Architecture

Sanjay Santokee
Nov 6 · 2 min read

Consider the following:

We want 13-bit floating point representation of 27.37

with a 5 bit Bias

Format is : Sign _ , Biased Exp _ _ _ _ _ , Significand _ _ _ _ _ _ _

Actual Exp is also referred to as True Exp


Bias = 2^(k-1) — 1

Biased Exp = True Exp + Bias

So, True Exp = Biased Exp — Bias


Calculate 27.37 in Decimal:

27.37 = 11011.010


Calculate Bias in Decimal:

Bias = ²⁴ — 1 = 15


Normalize The Significand and gain True Exp

it is always in the format 1.significand

so, we get 1.1011010 x 2⁴ (which is taking the 11011.010 above and moving the point to the first position after the first “1”

4 is the “power” or superscript because the point was moved four places to the left.

The 4, which is the superscript of any normalized binary number, would be the True Exp.

So, True Exp = 4


Calculate Biased Exp:

Biased Exp = True Exp + Bias

Biased Exp = 4 + 15

Biased Exp = 19


Finding the Biased Exp in Binary:

19 = 10011


Assemble components into FP Format

Sign- positive since it is 27.37

Biased Exp- 10011

Significand- 1011010


Finding the Floating Point representation:

0 10011 1011010

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