Hexadecimal to decimal with place values 1, 16, 256
The places of a hexadecimal number are worth powers of 16, counted from the right: 16⁰ = 1, 16¹ = 16, 16² = 256 and 16³ = 4096. To convert to decimal, replace each letter by its value, multiply each digit by the value of its place, and add. For (2A5)₁₆ the digits 2, A and 5 stand in the places worth 256, 16 and 1, and A means 10, so (2A5)₁₆ = 2×256 + 10×16 + 5×1 = 512 + 160 + 5 = 677 in decimal. A letter must be replaced by its value before multiplying: the A in 2A5 is worth 10. The biggest number with two hexadecimal symbols is FF, which is 255, the same as the biggest number a byte can show.
| Place value | 256 | 16 | 1 |
|---|---|---|---|
| Power of 16 | 16² | 16¹ | 16⁰ |
| Digit of 2A5 | 2 | A = 10 | 5 |
| Digit × value | 512 | 160 | 5 |
| Place value | 16 | 1 |
|---|---|---|
| Digit | E = 14 | 7 |
| Digit × value | 224 | 7 |
Choose three hexadecimal numbers of two or three symbols, with a letter in at least two of them. Convert each to decimal on paper with a table of place values.