3F7₁₆ → decimal — number base conversion
corepositional expansion in base 16
Answer
1015
Why this example is worth doing
Hexadecimal to decimal by positional weights, with the digit F standing for fifteen. The page's specific contribution here is the letter digits: A to F are digits, not variables, and the reason base sixteen needs them is that positional notation requires exactly as many digit symbols as the radix. Stating that explicitly turns the letters from an arbitrary convention into a consequence.
Try your own input in the Binary ⇄ decimal ⇄ hex ⇄ octal. Convert between any two bases, integers and fractions, with the positional working.
How the answer is reached
Base 16 to base 10
Convert 3F7 from base 16 to base 10. The sign is carried across unchanged; only the magnitude is converted.
| digit | value | weight | weight (base 10) | digit x weight |
|---|---|---|---|---|
| 3 | 3 | 16^2 | 256 | 768 |
| F | 15 | 16^1 | 16 | 240 |
| 7 | 7 | 16^0 | 1 | 7 |
| total | 1015 |
Integer part: divide by 10 and read the remainders bottom to top.
| n | divide by | quotient | remainder |
|---|---|---|---|
| 1015 | 1015 ÷ 10 | 101 | 5 |
| 101 | 101 ÷ 10 | 10 | 1 |
| 10 | 10 ÷ 10 | 1 | 0 |
| 1 | 1 ÷ 10 | 0 | 1 |
3F7 (base 16)1015 (base 10)