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Hardware/Binary/Hexadecimal_number_system.md
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@ -45,6 +45,10 @@ This table shows the raw value of each hexadecimal place value:
| -------- | -------- | -------- | -------- | | -------- | -------- | -------- | -------- |
| 4096 | 256 | 16 | 1 | | 4096 | 256 | 16 | 1 |
## Hexadecimal prefix
The custom is to prefix a hexadecimal number with `0x` to indicate that the number is hexadecimal.
## Converting hexadecimal numbers ## Converting hexadecimal numbers
Using the previous table we can convert hexadecimal values to decimal. Using the previous table we can convert hexadecimal values to decimal.
@ -59,13 +63,13 @@ $$
16^{n} \cdot 1,2,...F 16^{n} \cdot 1,2,...F
$$ $$
As applied to `1A5`: As applied to `0x1A5`:
| $16^{3}$ | $16^{2}$ | $16^{1}$ | $16^{0}$ | | $16^{3}$ | $16^{2}$ | $16^{1}$ | $16^{0}$ |
| ---------------------- | --------------------- | -------------------------- | ------------------- | | ---------------------- | --------------------- | -------------------------- | ------------------- |
| $1\cdot 16^{3} = 4096$ | $1\cdot 16^{2} = 256$ | $A (10)\cdot 16^{1} = 160$ | $5\cdot 16^{0} = 5$ | | $1\cdot 16^{3} = 4096$ | $1\cdot 16^{2} = 256$ | $A (10)\cdot 16^{1} = 160$ | $5\cdot 16^{0} = 5$ |
Another example for `F00F`: Another example for `0xF00F`:
$(15 \cdot 4096 = 61440) + (0 \cdot 256 = 0) + (0 \cdot 16 = 0) + (15 \cdot 1 = 15) = 61455$ $(15 \cdot 4096 = 61440) + (0 \cdot 256 = 0) + (0 \cdot 16 = 0) + (15 \cdot 1 = 15) = 61455$