Why can't we store exponent of IEEE floating point number without adding bias or converting it to 2's or 1's complement?

Question

Why do we have to add bias or convert an exponent of IEEE floating point number in its 2's or 1's complement form ?? why can't we store it like this in single precision :

1.1 * 2^0 => 0 00000000 10000000000000000000000

instead of this:

1.1 * 2^ (0 + 127) => 0 01111111 10000000000000000000000

thanks

I think you'll find a good answer [here](http://stackoverflow.com/questions/2612775/why-ieee-floating-point-number-calculate-exponent-using-a-biased-form?rq=1) — berna1111, Jan 26 '17 at 15:16
@PatriciaShanahan i would represent it in 1's or 2's complement — , Jan 26 '17 at 16:00

score 2 · Accepted Answer · answered Jan 26 '17 at 18:47

2

The bias format for the exponent let you do this nice trick:

Given a floating point f, denote with <f> its binary representation.
Denote with + the integer addition.

Then

<f> + 1 = nextafter(f)

towards the infinity of the same sign of f.

This is true as long as the sum doesn't affect the sign bit.

answered Jan 26 '17 at 18:47

Margaret Bloom

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It also simplifies comparisons in hardware. Ignoring NaNs, the order of magnitude of the floats matches the unsigned binary order of the bit patterns with the sign bit chopped off. – Patricia Shanahan Jan 26 '17 at 22:24
@PatriciaShanahan Very good point! – Margaret Bloom Jan 27 '17 at 09:20

Why can't we store exponent of IEEE floating point number without adding bias or converting it to 2's or 1's complement?

1 Answers1