Hexadecimal Number System / Decimal Number System (Base-10) / Octal Number System (Base-8) / Binary Number System (Base-2)
@. Hexadecimal Number System (Base-16)
1. Base: 16
o It uses 16 symbols:
0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F
Values of letters:
o A=10, B=11, C=12, D=13, E=14, F=15.
2. Place values:
o Like decimal uses powers of 10, hexadecimal uses powers of 16
@. Decimal Number System (Base-10)
1. Base: 10
o It uses 10 symbols (digits):
0,1,2,3,4,5,6,7,8,9
2. Place values:
o Each position represents a power of 10.
3. Why called “decimal”?
o “Deci” means 10.
o Based on 10 digits → our everyday number system.
4. Where used ?
o It is the standard system we use in daily life for counting, money, measurement, etc.
In short:
1. Decimal = base 10 system
2. Digits = 0–9
3. Place values = powers of 10
@. Octal Number System (Base-8)
1. Base: 8
o It uses 8 symbols (digits):
0,1,2,3,4,5,6,7
2. Place values:
o Each position represents a power of 8.
3. Relation with binary:
o 1 Octal digit = 3 Binary digits.
4. Why useful?
o Easier shorthand for binary numbers (shorter than writing long binary).
o Example:
§ Binary: (110101)2
§ Octal: (65)8
In short:
1. Octal = base 8 system
2. Digits = 0–7
3. Place values = powers of 8
@. Binary Number System (Base-2)
1. Base: 2
o Uses only two digits: 0 and 1
2. Place values:
o Each position is a power of 2.
3. Why important ?
o Computers use binary because circuits have two states:
§ 0 = OFF
§ 1 = ON
In short:
1. Binary = base 2 system
2. Digits = 0, 1
3. Place values = powers of 2