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Converting Any Base to Decimal
Multiply each digit by its place value and add the results. The same method works for binary, octal and hexadecimal.
One Method for Every Base
To turn a number in any base into decimal:
- Write the number with each digit in its own column.
- Above each digit, write its place value — the base to the power 0, 1, 2 … counting from the right.
- Multiply each digit by its place value.
- Add the results.
This is called the place-value method (or the positional method).
Binary to Decimal
Octal to Decimal
Hexadecimal to Decimal
For hex, first change any letters into their decimal values (A = 10, B = 11, C = 12, D = 13, E = 14, F = 15). Then use the same method with place values 1, 16, 256, 4096 …
Number base converter
Binary (2)
1110011011
Octal (8)
1633
Decimal (10)
923
Hex (16)
39B
Working: multiply each digit by its place value, then add
| Digit | Place value | Digit × place value |
|---|---|---|
| 1 | 29 = 512 | 1 × 512 = 512 |
| 1 | 28 = 256 | 1 × 256 = 256 |
| 1 | 27 = 128 | 1 × 128 = 128 |
| 0 | 26 = 64 | 0 × 64 = 0 |
| 0 | 25 = 32 | 0 × 32 = 0 |
| 1 | 24 = 16 | 1 × 16 = 16 |
| 1 | 23 = 8 | 1 × 8 = 8 |
| 0 | 22 = 4 | 0 × 4 = 0 |
| 1 | 21 = 2 | 1 × 2 = 2 |
| 1 | 20 = 1 | 1 × 1 = 1 |
512 + 256 + 128 + 0 + 0 + 16 + 8 + 0 + 2 + 1 = 923
Answer: 11100110112 = 92310
Practice
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More lessons in Number Systems · Next: Decimal to Binary, Octal and Hexadecimal · Previous: Why Computers Use Binary