Binary number system
Octal number system
Consists of eight digits ranging from 0-7.the place value of octal numbers goes up in factors of eight from right to left.
Hexadecimal number system
This is a base 16 number system that consists of sixteen digits ranging from 0-9 and letters A-F where A is equivalent to 10,B to 11 up to F which is equivalent to 15 in base ten system. The place value of hexadecimal numbers goes up in factors of sixteen.
- A hexadecimal number can be denoted using 16 as a subscript or capital letter H to the right of the number .For example, 94B can be written as 94B16 or 94BH.
Further conversion of numbers from one number system to another
- To convert numbers from one system to another. the following conversions will be considered.
- Converting between binary and decimal numbers.
- Converting octal numbers to decimal and binary form.
- Converting hexadecimal numbers to decimal and binary form.
- a) Conversion between binary and decimal number
- Converting binary numbers to decimal numbers
- To convert a binary number to a decimal number, we proceed as follows:
- First, write the place values starting from the right hand side.
- Write each digit under its place value.
- Multiply each digit by its corresponding place value.
- Add up the products. The answer will be the decimal number in base ten.
EXAMPLE
Convert 1011012 to base 10(or decimal) number
|
Place value |
25 |
24 |
23 |
22 |
21 |
20 |
|
Binary digits |
1 |
0 |
1 |
1 |
0 |
1 |
Multiply each digit by its place value
|
N10=(1*25) +(0*24)+(1*23)+(1*22)+(0*21)+(1*20) N10=32+0+8+4+0+1
=4510 |
32*1=32
16*0=0
8*1=8 4*1=4
2*0=0
1*1=1
=4510
NB: remember to indicate the base subscript since it is the value that distinguishes the different systems.