Basics: signed an unsigned information

Basics

Signed an unsigned information

When bytes, wydes, tetras and octas represent numbers, they can be signed or unsigned. In the last case the most significant bit stores the sign of the number: 0 codes plus and 1 - minus.

Negative numbers are stored in memory in a special way called complement code. To get this code for negative integer do the following:

in absolute value of the binary number change every digit to the opposite: 0 to 1 and 1 to 0
add 1 to the result

Such manner of coding provides the easement of arithmetic operations inside a computer.

Example
Let's convert -127 into complement code:
127₁₀ = 0111 1111₂
invert: 1000 0000
add 1: 1000 0001₂ = 81₁₆
The coding of several characteristic numbers is shown in the table below.

contents of byte (hex)	00	01	...	7F	80	81	...	FE	FF
unsigned number (decimal)	0	1	...	127	128	129	...	254	255
signed number (decimal)	0	1	...	127	-128	-127	...	-2	-1

You can see that an unsigned byte is a number between 0 and 2⁸ - 1 = 255 inclusive. A signed integer lies between -128 and +127 inclusive.

Similar situation takes place for wydes, tetras and octas.

unit	size	minimum / maximum
	(bits)	unsigned		signed
byte	8	0	2⁸ - 1 = 255	-128	127
wyde	16	0	2¹⁶ - 1 = 65 535	-32 768	32 767
tetra	32	0	2³² - 1 = 4,294,967,295	-2,147,483,648	2,147,483,647
octa	64	0	2⁶⁴ - 1 = 18,446,744,073,709,551,615	-9,223,372,036,854,775,808	9,223,372,036,854,775,807

Related topics:

"MMIX basics" page