Offset Binary

numeric

Definition

Offset Binary

Offset Binary is a method for signed number representation where a signed number n is represented by the bit pattern corresponding to the unsigned number , being the biasing value or offset.

¹

Symmetry

There are two types of offset binary: symmetric and asymmetric offset.

Symmetric Offset

The Symmetric offset adds a single constant excess to all numbers:

The goal is to represent negative numbers as positive numbers. They don’t need to be stored as signed numbers. Thus, all numbers are representable by an excess if .

The excess is derived from the smallest representable negative number:

Example:

Actual Value	Calculation	Offset Binary Code	Binary Representation
-4	-4 + 4 = 0	0	000
-3	-3 + 4 = 1	1	001
-2	-2 + 4 = 2	2	010
-1	-1 + 4 = 3	3	011
0	0 + 4 = 4	4	100
1	1 + 4 = 5	5	101
2	2 + 4 = 6	6	110
3	3 + 4 = 7	7	111

For an unsigned bit pattern of bit length , the excess is always:

Asymmetric Offset

Arithmetic

Addition

Let b the excess, and and , adding these two excess-numbers is equal to:

Wrong:

Correct:

Footnotes

1. Offset binary - Wikipedia ↩