Base Conversion Process
This page goes through the steps for converting a number from decimal to binary, and binary to decimal.
When asked to explain your process, use words. Follow the steps that we’ve listed out for you!
Binary and Decimal as Positional Number Systems
| Decimal digits: | 1 | 7 | 9 |
| Position Value | 100 | 10 | 1 |
17910 = 1*100 + 7*10 + 9*1
| Binary digits: | 1 | 1 | 0 | 1 |
| Position Value: | 8 | 4 | 2 | 1 |
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 you would write 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