Base Conversion Process

This page goes through the steps for converting a number from decimal to binary, and binary to decimal.

Binary and Decimal as Positional Number Systems

Decimal digits:179
Position Value100101

17910= 1*100 + 7*10 + 9*1

Binary digits:1101
Position Value:8421

11012= 1*8 + 1*4 + 0*2 + 1*1 = 1310


Convert the DECIMAL number 45 to BINARY

1. Write the position values, from right to left. Stop when youwouldwrite a number that is greater than the given number, and write up to the one before it. (In this case, stop at 64, and write 32).

? ? ? ? ? ?
32 16 8 4 2 1

 

2. Starting at the left, add each value that keeps the sum less than or equal to the given decimal value by placing a 1.

1 ? ? ? ? ?
32 16 8 4 2 1

 

3. Subtract the position values from the given number

45 – 32 = 13. 16 > 13, so it will have a 0.

Repeat Steps 2 and 3 until you have an answer.

4. Write down your answer

4510= 1011012


Convert the BINARY number 00010101 to DECIMAL

1. Write the binary digits in order (from left to right)

Example: 00010101

2. Write the position values underneath the binary digits (from right to left)

Example:

1 0 1 0 1
16 8 4 2 1

(It’s OK to exclude leading 0’s)

3. Multiply the position values with its binary partner and add them together

Example: (16*1) + (8*0) + (4*1) + (2*0) + (1*1) = 21

4. Write down your answer

Example: 2110= 000101012


Examples (Try it!)

Convert binary to decimal

A. 00010100

B. 10110101

C. 01011011

D. 10111010

Convert decimal to binary

A. 42

B. 75

C. 145

D. 250

Answers

A: 20 B: 181 C: 91 D: 186

A: 101010 B: 1001011 C: 10010001 D: 11111010