1. Base ‘b’ number for i = 0 to n – 1 for an n digit quantity
In general a number system can have any base b
the digit used are 0, 1, … , b-1
The weight of ith place is bi
The conversion formula from base b into decimal number is
Commonly used base are 2, 3, 8, 10, 16, ...
for i = 0 to n – 1
for an n digit quantity

2. Bases 2, 8, and 16 are related

3. Conversion From binary to octal
make groups of 3 bits from right to left
 1668
From octal to binary
make each digit as 3 bits sequence
2768 
From binary to hexadecimal
make groups of 4 bits from right to left
 7616
From hexadecimal to binary
make each digit as 4 bits sequence
3716 

4. More on Conversion Convert from base b1 to decimal
Convert from decimal to base b2
Direct conversion from base b1 and base b2
we will not pursue this anymore
Decimal to Hexadecimal
Divide by 16 recursively and collect digit from right to left from the remainders.
Example = D8F16
3471 divided by 16 gives 216, remains 15 (F)
216 divided by 16 gives 13, remains 8 (8)
13 divided by 16 gives 0, remain 13 (D)