A regular decimal is the sum of the digits multiplied by a power of 10.
137 in base 10 is equal to each digit multiplied by the corresponding power of [10].
13710 = 1×102+3×101+7×100 = 100+30+7
Hex numbers are read the same way, but each digit counts power of 16 instead of power of 10.
For hex number with n digits:
dn-1 ... d3 d2 d1 d0
Multiply each digit of the hex number with its corresponding power of 16 and sum:
decimal = dn-1×16n-1 + ... + d3×163 + d2×162 + d1×161+d0×160
3A in base 16 is equal to each digit multiplied with its corresponding 16n:
(3A)₁₆ = (3 × 16¹) + (10 × 16⁰) = (58)₁₀
3C in base 16 is equal to each digit multiplied with its corresponding 16n:
(3C)₁₆ = (3 × 16¹) + (12 × 16⁰) = (60)₁₀
E7A8 in base 16 is equal to each digit multiplied with its corresponding 16n:
(E7A8)₁₆ = (14 × 16³) + (7 × 16²) + (10 × 16¹) + (8 × 16⁰) = (59304)₁₀
0.9 in base 16:
(0.9)₁₆ = (0 × 16⁰) + (9 × 16⁻¹) = (0.5625)₁₀
| Hex base 16 | Decimal base 10 | Calculation |
|---|---|---|
| 0 | 0 | - |
| 1 | 1 | - |
| 2 | 2 | - |
| 3 | 3 | - |
| 4 | 4 | - |
| 5 | 5 | - |
| 6 | 6 | - |
| 7 | 7 | - |
| 8 | 8 | - |
| 9 | 9 | - |
| A | 10 | - |
| B | 11 | - |
| C | 12 | - |
| D | 13 | - |
| E | 14 | - |
| F | 15 | - |
| 10 | 16 | 1×161+0×160 = 16 |
| 11 | 17 | 1×161+1×160 = 17 |
| 12 | 18 | 1×161+2×160 = 18 |
| 13 | 19 | 1×161+3×160 = 19 |
| 14 | 20 | 1×161+4×160 = 20 |
| 15 | 21 | 1×161+5×160 = 21 |
| 16 | 22 | 1×161+6×160 = 22 |
| 17 | 23 | 1×161+7×160 = 23 |
| 18 | 24 | 1×161+8×160 = 24 |
| 19 | 25 | 1×161+9×160 = 25 |
| 1A | 26 | 1×161+10×160 = 26 |
| 1B | 27 | 1×161+11×160 = 27 |
| 1C | 28 | 1×161+12×160 = 28 |
| 1D | 29 | 1×161+13×160 = 29 |
| 1E | 30 | 1×161+14×160 = 30 |
| 1F | 31 | 1×161+15×160 = 31 |
| 20 | 32 | 2×161+0×160 = 32 |
| 30 | 48 | 3×161+0×160 = 48 |
| 40 | 64 | 4×161+0×160 = 64 |
| 50 | 80 | 5×161+0×160 = 80 |
| 60 | 96 | 6×161+0×160 = 96 |
| 70 | 112 | 7×161+0×160 = 112 |
| 80 | 128 | 8×161+0×160 = 128 |
| 90 | 144 | 9×161+0×160 = 144 |
| A0 | 160 | 10×161+0×160 = 160 |
| B0 | 176 | 11×161+0×160 = 176 |
| C0 | 192 | 12×161+0×160 = 192 |
| D0 | 208 | 13×161+0×160 = 208 |
| E0 | 224 | 14×161+0×160 = 224 |
| F0 | 240 | 15×161+0×160 = 240 |
| 100 | 256 | 1×162+0×161+0×160 = 256 |
| 200 | 512 | 2×162+0×161+0×160 = 512 |
| 300 | 768 | 3×162+0×161+0×160 = 768 |
| 400 | 1024 | 4×162+0×161+0×160 = 1024 |
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