Hex 2 Binary 2 Octal Transforming Numerical Systems

Lesson 7: Hex 2 Binary 2 Octal

General Method for Transforming Numbers - Number we want to transform uses base X: we would like to transform this number into new one, that uses Y base. In this case we will use method of continuous dividing and multiplying (dividing numbers left of comma (,) with Y and multiplying numbers on the right side of comma, by Y - rational numbers). This method is best understood looking at these examples:

Octal System:

Base: 8
Digits: 0, 1, 2, 3, 4, 5, 6, 7
Example: 27 (decimal) = 33 ₈ (octal)

Hexadecimal (hex) System:

Base: 16
Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
Example: 27 (decimal) = 1B ₁₆ (hex)


Binary System:

Base: 2
Digits: 0, 1
Example: 27 (decimal) = 11011 ₂ (binary)


Transforming Binary, Hex and Octal - Quickly

Binary Hex Binary Octal

0000 0 000 0
0001 1 001 1
0010 2 010 2
0011 3 011 3
0100 4 100 4
0101 5 101 5
0110 6 110 6
0111 7 111 7
1000 8
1001 9
1010 A
1011 B
1100 C
1101 D
1110 E
1111 F

Example

Transform -6F,A ₁₆into binary number

-6F,A 16 = - 0110 1111 , 1010 2 = - 1101111 , 101 2

Example

Transform 11,000011001 ₂into hex number

11,000011001 2 = 11 , 0000 1100 1 2
 = 0011 , 0000 1100 1000 2
 = 3 , 0 C 8 16
 = 3 , 0C8 16

Example

Transform 37,24 ₈into binary number

37,24 8 = 011 111 , 010 100 2 = 11111 , 0101 2

Example

Transform 1111011,10011101 ₂ into octal number

1111011,10011101 2 = 1 111 011 , 100 111 01 2
 = 001 111 011 , 100 111 010 2
 = 1 7 3 , 4 7 2 16
 = 173 , 472 16