What is Number System?

• System of writing and representing numbers in different forms
• Covers the way of writing numbers and associated operations

Decimal Numbers

• Has 10 digits - 0 to 9, that means, Radix = 10

Example,
2024 = 2 * 1000 + 0 * 100 + 2 * 10 + 4 * 1

• Individual number is digit

2	0	2	4
d3	d2	d1	d0

• Use in real life taking the fact into consideration that we have 10 fingers and it is convenient to count with them as decimal uses 10 digits from 0 to 9
• Counting starts like 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, then 10, 11 , 12 … . It becomes two digits, then three like 101, 102, … and so on.

Binary Numbers

• Efficient number system used by computers.
• Radix = 2, i.e., we use two digits - 0 and 1
• 0 and 1 are the representation of the lower and higher voltages at the hardware level, mainly with CPU

Example, Take number 1101
We can write it as (1101)_{base 2} - the subscript is used to determine which base the number belongs to, in this case base 2 is written, that means 0 and 1 are the only digits being used to write these number.

1	1	0	1
d3	d2	d1	d0

• d0 is the least significant digit, any digit at position zero is least significant digit.

Hexadecimal Numbers

• Mostly used for easy and short representation of binary numbers
• Radix = 16, Hexadecimal Numbers uses 16 digits - 0 to 9 and A to F
• A to F are equivalent to 10 to 15 in decimal

A _{base 16} = 10 _{base 10}
B _{base 16} = 11 _{base 10}
C _{base 16} = 12 _{base 10}
D _{base 16} = 13 _{base 10}
E _{base 16} = 14 _{base 10}
F _{base 16} = 15 _{base 10}

Example, 6D1A

6	D	1	A
d3	d2	d1	d0

We can make any base number, there is Octal number also, it has 8 digits. There can be as many as you wish to make, we can make 19 digits, 25 digits

These 4 - Decimal, Binary, Hexadecimal and Octal are standard.