Hexadecimal Numbers
Hexadecimal (hex) offers a nice, compact way to represent binary numbers.
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The prefix 0x is used to indicate a hexadecimal number.
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Each hex digit represents a nibble (4 bits).
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Each nibble is guaranteed to be a number from 0-15; 0-F in hex.
Using four bits to represent hex digits: logic.ly
When you see the hexadecimal prefix (0x), know that you're looking at a hex number - even though you're not seeing the zeroes and ones.
Example: 0x24 does not equal (24)10.
Convert: Binary to Hex
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Break binary number into groups of 4 bits (called a nibble).
Convert each nibble to binary then to hex.
Concatenate the results - put them back together.
Convert the binary number to hexadecimal: (11011100)2
- Break binary number into groups of 4 bits:
- 1101
- 1100
- Convert each nibble to decimal:
- (1101)2 = 13
- (1100)2 = 12
- Convert each decimal nibbles to hex:
- 13 = D
- 12 = C
- Concatenate the results (don't forget the 0x prefix!):
0xDC
Convert: Hex to Binary
For hex to binary, we simply go the other direction - take each hex digit and convert it its binary equivalent.
Example 1
Convert the hexadecimal number to binary: 0x24
When we see 0x24, we're looking at a byte (8 bits):
| 2 | 4 | |||||||
|---|---|---|---|---|---|---|---|---|
| ? | ? | ? | ? | ? | ? | ? | ? |
So we convert to binary...
2 = (0010)2
4 = (0100)2
Then plug in the result:
| 2 | 4 | |||||||
|---|---|---|---|---|---|---|---|---|
| 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 |
Final result = 00100100
Example 2
Convert the hexadecimal number to binary: 0xA1
Nothing different here, we just have to know that the letters represent numbers.
A = (10)10 = (1010)2
1 = (1)10 = (0001)2
Plugging in:
| A | 1 | |||||||
|---|---|---|---|---|---|---|---|---|
| 1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 |
Final result = 10100001