Chapter 2 Number System Base

Number System Base

- A base for a number system is the maximum number that can be represented in the single digit or number.
- A number system is a set of rules and symbols used to represent a number.
- There are several types of number system but we are here only focus on:
a) Binary (base 2)
b) Decimal (base 10)
c) Hexadecimal (base 16)
- Below is a table of values that you need to memorize.

A) Binary Number System
- The prefix "bi-" stands for 2
- The binary number system is a Base 2 number system.
- There are 2 symbols that represent quantities: 0, 1
- Each place value in a binary number is a power of 2.

1110 10112 = (1x2⁷)+(1x2⁶)+(1x2⁵)+(0x2⁴)+(1x2³)+(0x2²)+(1x2¹)+(1x2⁰)

                 = 128+64+32+8+2+1

                 = 23510

                 = E B16

1 01112 = (1x2⁴)+(0x2³)+(1x2²)+(1x2¹)+(1x2⁰)
             = 16+4+2+1
             = 2310
             = 1716

B) Decimal Number System

- The prefix "deci-" stands for 10.
- The decimal number system is a Base 10 number system.
- There are 10 symbols that represent quantities : 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
- Each place value in a decimal number is a power of 10.
8810 = 64 + 0 + 16 + 8 + 0 + 0 + 0
       = (1x2⁶)+(0x2⁵)+(1x2⁴)+(1x2³)+(0x2²)+(0x2¹)+(0x2⁰)
       = 10110002
       = 5816 

C) Hexadecimal Number System
- The prefix "hexa-" stand for 16
- The decimal number system is a Base 16 number system.
- There are 16 symbols that represent quantities : 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F.
- Each place value in a hexadecimal number is a power of 16.

B916 = 101110012
        =  (1x2⁷)+(0x2⁶)+(1x2⁵)+(1x2⁴)+(1x2³)+(0x2²)+(0x2¹)+(1x2⁰)
        = 128+0+32+16+8+0+0+1
        = 18510