next up previous contents
Next: Boolean Algebra Up: Number Systems Previous: BinaryOctal and Hexadecimal

Number Representation

We define the following

word: a binary number consisting of an arbitrary number of bits.
nibble: a 4-bit word (one hexadecimal digit).
byte: an 8-bit word.

We often use the expressions 16-bit word (short word) or 32-bit word (long word) depending on the type of computer being used. Most fast computers today actually employ a 64-bit word at the hardware level.

If a word has n bits it can represent different numbers in the range 0 to . Negative numbers are usually represented by the so called 2's complement notation. To obtain the 2's compliment of a number first take the complement (invert each bit) and then add 1. All the negative numbers will have a 1 in the MSB position, and the numbers will now range from to . The electronic advantages of the 2's complement notation becomes evident when addition is performed. Convince yourself of this advantage.

Doug Gingrich
Tue Jul 13 16:55:15 EDT 1999