Hexadecimal and How to Use It
08/31/2001
To start with, "Hexadecimal" simply means "hex (6) above decimal (10)", or "6 more than decimal".
Hexadecimal is one of a number of binary codes, and it would be well to look closely at this aspect in the right way, to keep from getting unnecessarily lost. There are some key terms that we should also have in mind as we go.
- Weighted Values
- Each binary bit has an assigned value, depending on its placement or position.
- Positional Weights
- Where that binary bit is placed determines its weighted value.
Note that the 421 or the 8421 does represent a simple "weighted value" for any bit that happens to be in that "position", hence the term "Positional Weight".
| # | Octal | BCD | Hexadecimal | Excess-3 | Self-Compl | Auto-Round |
|---|---|---|---|---|---|---|
| 4 2 1 | 8 4 2 1 | 8 4 2 1 | 8 4 2 1 | 2'4 2 1 | 5'4 2 1 | |
| 0 | 0 0 0 | 0 0 0 0 | 0 0 0 0 | 0 0 1 1 | 0 0 0 0 | 0 0 0 0 |
| 1 | 0 0 1 | 0 0 0 1 | 0 0 0 1 | 0 1 0 0 | 0 0 0 1 | 0 0 0 1 |
| 2 | 0 1 0 | 0 0 1 0 | 0 0 1 0 | 0 1 0 1 | 0 0 1 0 | 0 0 1 0 |
| 3 | 0 1 1 | 0 0 1 1 | 0 0 1 1 | 0 1 1 0 | 0 0 1 1 | 0 0 1 1 |
| 4 | 1 0 0 | 0 1 0 0 | 0 1 0 0 | 0 1 1 1 | 0 1 0 0 | 0 1 0 0 |
| 5 | 1 0 1 | 0 1 0 1 | 0 1 0 1 | 1 0 0 0 | 1 0 1 1 | 1 0 0 0 |
| 6 | 1 1 0 | 0 1 1 0 | 0 1 1 0 | 1 0 0 1 | 1 1 0 0 | 1 0 0 1 |
| 7 | 1 1 1 | 0 1 1 1 | 0 1 1 1 | 1 0 1 0 | 1 1 0 1 | 1 0 1 0 |
| 8 | 1 0 0 0 | 1 0 0 0 | 1 0 1 1 | 1 1 1 0 | 1 0 1 1 | |
| 9 | 1 0 0 1 | 1 0 0 1 | 1 1 0 0 | 1 1 1 1 | 1 1 0 0 | |
| A | 1 0 1 0 | |||||
| B | 1 0 1 1 | |||||
| C | 1 1 0 0 | |||||
| D | 1 1 0 1 | |||||
| E | 1 1 1 0 | |||||
| F | 1 1 1 1 |
Note that A-F represent 6 numerical values beyond the 0-9 decimal values.
Octal is simply a binary code that goes from 0 to 7, which are 8 possible states.
Binary Coded Decimal is simply a binary code that goes from 0 to 9, which are 10 possible states.
"Excess-3" is actually a special BCD code that is "Self-Complimenting and "Automatic-Rounding"
The 2'421 is actually a special BCD code that is "Self-Complimenting" (more about this later).
The 5'421 is another special BCD code that is for "Automatic Rounding" (more about this later).
- Many folks that try to learn or memorize Hex Values, simply try too hard. It's fairly easy to learn the binary codes from 0-9, but then they struggle with the remaining 6 codes.
- Look at this interesting point - "A" represents a decimal value of 10, and the binary pattern looks something like "10, 10".
- Next, notice that "F" is obviously a "Full-House" (1111).
- I have found that the only one you should try to memorize is "C" - (1100) !! Isn't that a whole lot easier than trying to memorize all 6 of them?
- Now, it doesn't take a genius to realize that "B" is simply one more than "A", and so therefore one more than 1010 must be 1011.
- In that same respect, one more than our memorized "C" (1100) must be "D" (1101).
- Finally, realizing that "E" is simply one less than the "F" (1111), it must be 1110.
- If you have followed all of this then you are already there! You now know Hex codes.
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