OCR Computing A-Level Revision

Number Systems (1.3.a)

The relationship between a digit, its position, and the base of the number system is expressed by a simple formula:

DIGIT * BASE POSITION

Download a free excel number base calculator which works for up to base-36, based on the above equation.

Octal

Octal is base-8. You can convert from binary to octal and back without "going through" decimal, by converting 3 binary bits to 1 octal bit, because 3 binary bits can represent up-to decimal 7, as can 1 octal bit.

  128 64 32 16 8 4 2 1  
  1 0 1 1 1 0 1 0 (186)
64 8 1  
2 7 2 (186)

Hexadecimal

Hexadecimal is base-16. Like with octal, you can convert from binary to hexadecimal (and back), by using 1 hexadecimal bit to represent 4 binary bits.

Binary-Coded Decimal (BCD)

Binary-Coded Decimal (BCD) is when the individual decimal digits are represented using 4 binary bits.

100 10 1  
1 2 9 (129)
8 4 2 1 8 4 2 1 8 4 2 1  
0 0 0 1 0 0 1 0 1 0 0 1 (129)