# Unsigned binary integers

Unsigned binary integers are numbers without any ‘+’or ‘-’ sign. Here all bits representing the number will represent the magnitude part of the number only. No bits will remain reserved for sign bit representation. An unsigned binary integer is a fixed-point system with no fractional digits.

Some real life Examples are −

• Number of tables in a class,

• The number of a member of a family.

Obviously, they are unsigned integers like 10 and 5. These numbers have to be represented in a computer using only binary notation or using bits.

Numbers are represented in a computer using a fixed size, like 4, 8, 16, 32 bits, etc. If numbers are represented in a computer using 8 bits, it is said that the computer uses 8-bit word size. Generally, word sizes are a power of 2. Modern computers typically support binary integers of 8 (i.e. 23),16 (i.e. 24),32 (i.e. 25),or 64 (i.e. 26)bits.A tabular column of some decimal numbers and their equivalent in unsigned binary is shown in the following, assuming a word size of 4bits.

Number
Unsigned binary notation
5
0101
13
1101
0
0000 Minimum number, which is 0
15
1111 Maximum number, which is (24 -1)

In this table,

5 in binary representation is −

 2 5 2 2 Remainder 1 2 1 Remainder 0 2 0 Remainder 1

So it is − 0101

And 0101 in decimal representation is − 0*23 +1*22 +0*21 +1*20

From this, it is obvious that if the word size is n bits, the range of (2n –1) numbers can be represented as ranging from 0 to (2n –1). A table of word size and the range of unsigned integers that can be represented is shown here –

Word size
The range for unsigned numbers
4
0 to 24- 1 or 0 to 15
8
0 to 28- 1 or 0 to 255
16
0 to 216- 1 or 0 to 65535
32
0 to 232- 1 or 0 to 4,294,967,295
64
0 to 264-1 or 0 to 1.844674407x 1019

In other words, when the word size is only 4 bits, it is not possible to represent a number like 223. The minimum word size has to be 8 bits to represent the number 223.