"http://www.physics.udel.edu/~watson/scen103/colloq2000/hex.html"
Last updated April 12, 2000.
© George Watson, Univ. of Delaware, 2000.
Silicon, Circuits, and the Digital Revolution
Hexadecimal Numbers
Hex for short
Binary numbers can be unwieldy in length
Place holders are powers of 16
| Power of 16: | 3 | 2 | 1 | 0 |
|---|---|---|---|---|
| Weight: | 4096 | 256 | 16 | 1 |
Sixteen symbols or characters needed:
The usual 10 of 0, 1, 2, ... 9 plus A, B, C, D, E, and F
Correspondence between new hexadecimal digits and decimal/binary
| Decimal | Hex | Binary |
|---|---|---|
| 10 | A | 1010 |
| 11 | B | 1011 |
| 12 | C | 1100 |
| 13 | D | 1101 |
| 14 | E | 1110 |
| 15 | F | 1111 |
4 bits used to represent a single hex digit
Example: conversion of 7CE to decimal.
| 7CE = | (7 x 162) + (C x 16) + E |
| = | (7 x 256) + (12 x 16) + 14 |
| = | 1792 + 192 + 14 |
| = | 1998 |
If there is any likelihood of confusion, the base of the number system should be indicated by explicitly writing the radix. For example, the answer above, decimal 1998, would be more precisely written as 199810. Hexadecimal numbers are typically indicated by using the subscript H behind the number; in the example above 7CEH was converted to a decimal number. Note that 1998 would be ambiguous if written in a context where the counting base is not clear; is 1998H or 199810 intended?
Example: conversion of 7CE to binary.
| 7CE = | 0111 1100 1110 |
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Comments, suggestions, or requests to ghw@udel.edu.
"http://www.physics.udel.edu/~watson/scen103/colloq2000/hex.html" Last updated April 12, 2000. © George Watson, Univ. of Delaware, 2000. |