Positional value representation systems

- Best known positional system is
**decimal number system** - Value of a digit depends on its position in number:
- There are
**10**digits in use: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 - Value of digits increase by
**10**for each position - Hence it is called the
**decimal**(10) number system

Example: 679 6 is in hundreds position (600) 7 is in tens position (70) 9 is in ones position (9) 679 ^^^ ||| ||| ||+--- value at 1: 9 x 1 = 9 |+---- value at 10: 7 x 10 = 70 +----- value at 100: 6 x 100 = 600 + -------- represented value = 679

- There are
- The computer uses the
**binary number system**: - Value of a digit depends on its position in number:
- There are
**2**digits in use: 0, 1 - Value of digits increase by
**2**for each position - Hence it is called the
**binary**(2) number system

Example 1:

1011 ^^^^ |||| |||+-- value at 1: 1 x 1 = 1 ||+--- value at 2: 1 x 2 = 2 |+---- value at 4: 0 x 4 = 0 +----- value at 8: 1 x 8 = 8 + -------- represented value = 11 (decimal)

Example 2:

11001 ^^^^^ ||||| ||||+-- value at 1: 1 x 1 = 1 |||+--- value at 2: 0 x 2 = 0 ||+---- value at 4: 0 x 4 = 0 |+----- value at 8: 1 x 8 = 8 +------ value at 16: 1 x 16 = 16 + -------- represented value = 25 (decimal)

- There are