2. Contents
Introduction to number system
Different bases numbers
Converting different bases numbers
into decimal
Converting decimal numbers into
different bases
Converting floating points
3. Objectives
At the end of this chapter, students
should be able to:
Explain the different bases number
system
Convert numbers into different bases
Convert floating numbers into different
bases
4. Introduction
Human
use decimal (base 10) number system to
count and perform arithmetic.
Computer
uses binary (base 2) number system.
each digit is known as a bit (0 and 1).
5. Introduction
Computer stores and manipulates the
bits in group of 8(byte), 16 (halfword),
32 (word) and 64 (double word).
Number of bits used in calculations
affects the accuracy and size
limitations of numbers manipulated by
the computer.
6. Introduction
Counting in base 10
E.g.: 0, 1, 2, 3, …, 10, …, 100,…
10 (1 x 101
+ 0 = 10 + 0)
63 (6 x 101
+ 3 x 100
= 60 + 3)
747 (7 x 102
+ 4 x 101
+ 7 x 100 =
700 + 40 + 7)
8. Different bases numbers
Number can be represented in different bases.
Different name of bases:
Base 2 binary
Base 3 ternary
Base 4 quaternary
Base 5 quinary
Base 6 senary
Base 7 septenary
Base 8 octal
Base 9 nonary
Base 10 decimal
Base 11 undenary
Base 12 duodecimal
Base 16 hexadecimal
Base 20 vigesimal
Base 60 sexagesimal
9. Different bases numbers
Base 2 includes (0, 1)
Base 3 includes (0,1,2)
Base 4 includes (0,1,2,3)
Base 9 includes ?
Base 12 includes ?
Base 16 includes?
10. Different bases numbers
Base 2 0,1, 10, 11,100, 101, …
Base 3 0,1,2, 10, 11, 12, 20, 21, …
Base 4 0,1,2,3,10,11,12, 13, 20, …
Base 9 ?
Base 12 ?
Base 16 ?