- the
*positional notation*of an*m*-digit, base*b*number (*b*進数) is

- its value is

- the largest value that can be represented is
*b*^{m}-1 - Example: an 8-digit, base 2 (binary) number (0-255)

- fixed-point numbers have the
*radix point*(小数点) at a specific position

- Example: an 8-digit, base 2 (binary) fixed-point number

- shifting a number one position to the left corresponds to
multiplying the number by the base
*b* - shifting a number one position to the right corresponds to
dividing the number by the base
*b**Example*

- overflow (オーバフロー) is always possible
- binary negative numbers are usually represented in
*2's complement*(2の補数系) or*1's complement*(1の補数系), because arithmetic operations are easier;*2's complement*is useful for calculations while*1's complement*is easier to compute

8-bit 2's complement 8-bit 1's complement Number Representation Number Representation 0 0 0 0 or 255 0 < *x*< 128*x*0 < *x*< 128*x*256-| *x*|255-| *x*|

*Examples (8-bit numbers)*

Decimal 2's Complement 1's Complement 37 00100101 00100101 -37 11011011 11011010