Base Conversion - Binary,Octal, Decimal, and Hexadecimal

A,B,C,D,E,and F in Hexadecimal

A = 10 B = 11 C = 12 D = 13 E = 14 F =15

Convert ANY base to base 10

Above each of the digits in the number, list the power of the base that the digits represents. It is now a simple process of multiplication and addition. Example: 235 _ 8 to base 10 5 x 8 ^ 0 = 5 3 x 8 ^ 1 = 24 2 x 8 ^ 2 = 128 5+24+128 = 157 235 _ 8 = 157 _ 10

Convert ANY base (B1) to ANY other base (B2) Where neither are base 10

B1 -> Base 10 -> B2

Decimal

Base 10

Hexadecimal

Base 16

Binary

Base 2

Octal

Base 8

Convert from Decimal to Binary

Divide by 2 and gather the remainders from last to first (or bottom to top). Divide until answer is 0. Example: 27 _ 10 to base 2 27/2 = 13 with r 1 13/2 = 6 with r 1 6/2 = 3 with r 0 3/2 = 3 with r 1 1/2 = 0 with r 1 = 11011 _ 2

Convert Hexadecimal to Decimal

Same method of converting ANY base to decimal but with 6 extra digits (A,B,C,D,E, and F)

Convert from Decimal to Any Other Base

Same method with conversion to Binary, divide by the BASE that is being converted to.

Finding remainder with calculator

Work the division normally, and round down the decimal form. Multiply the rounded number to divisor of original problem. Subtract that value from original number.