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: | 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 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