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.

In this table,

5 in binary representation is −

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 –

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.