16bit floating point

Question

I am having trouble understanding 16-bit floating points for an upcoming exam. I'm having the following digits in binary(after conversion);

+11100.111000₂ = 28.875₂. I got 28 easily, but how do I get '875' ?

Thanks

"get" in what way? algorithmically convert to a decimal string? — harold, Dec 20 '11 at 18:21
That doesn't look like floating point so much as an assumed decimal (binary?) point. If it were floating point, you wouldn't normally have a decimal point in the middle. — David Thornley, Dec 20 '11 at 18:29

score 1 · Answer 1 · answered Dec 20 '11 at 18:17

1

In a number, the value of a digit is multiplied by a constant, depending on the position. Let's take an example for a decimal number:

ab.cd₁₀ = a*10¹ + b*10⁰ + c*10^-1 + d*10^-2

It works similarly for binary numbers. For the portion to the right of the binary point in your example:

0.111000₂ = 2^-1 + 2^-2 + 2^-3 = 0.5 + 0.25 + 0.125 = 0.875.

answered Dec 20 '11 at 18:17

David Alber

Okay, that is right, however, where do I get those numbers from ? – Chris Arom Dec 20 '11 at 18:24
They are just 1/2, 1/4, 1/8 - just the reciprocal of the normal binary numbers – Martin Beckett Dec 20 '11 at 18:26
@ChrisArom Which numbers? The binary portion of my answer came from you. If you mean the 2^-1 (and so on), that is because it is a base-2 (i.e., binary) number. For base-10 (decimal) it would be 10^-1. For base-8 (octal) it would be 8^-1. – David Alber Dec 20 '11 at 18:30
Thanks guys, I got it now :) Time for more practice. – Chris Arom Dec 20 '11 at 18:44

score 1 · Answer 2 · answered Dec 20 '11 at 18:23

1

Left side of the . is multiply by 2, right side is divide by 2.

So you got 0.1110

0.1 = 0.5
0.01 = 0.25
0.001 = 0.125
----------------+
0.875

answered Dec 20 '11 at 18:23

Niels

2 Answers2