Lab Manual 01
Number Systems
Objectives
Students should be able to understand decimal, binary, octal and hexadecimal number systems.
The Binary Number System
The binary number system is a base 2 system with only two digits: 0 and 1. A binary number such as
“11010” is expressed with a string of 1s and 0s. The decimal equivalent of binary number can be
found by expanding the number into a power series with base of 2 e.g.
(11010)2 = 1x24 + 1x23 + 0x22 + 1x21 + 0x20
= 16 + 8 + 0 + 2 + 0
= (26)10
The binary system represents numbers using binary digits (bits) where each digit corresponds to a
power of two.
Another Example
Binary: 1 1 1 0 0 1 0 1
Power of two:2726 252423 222120
Decimal: 128 64 32 16 8 4 2 1
The total (in decimal) is 128 + 64 + 32 + 4 + 1 = 229
Since we begin counting from zero, n bits can represent 2n values:from 0 to 2n–1
inclusive (e.g. 256 values, from 0 to 255, for 8bits).
Groups of bits form binary words
Conversion from decimal to binary
Repeat division by 2
Example: Convert (29)10 to binary
– 29/2 = 14 remainder 1 (LSB)
– 14/2 = 7 remainder 0
– 7/2 = 3 remainder 1
– 3/2 = 1 remainder 1
– 1/2 = 0 remainder 1 (MSB)
(29)10 =>(11101)2
