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A repeated division and remainder algorithm can convert decimal to binary, octal, or hexadecimal.
Here is an example of using repeated division to convert 1792 decimal to binary:
Decimal Number | Operation | Quotient | Remainder | Binary Result | |
1792 | ÷ 2 = | 896 | 0 | 0 | |
896 | ÷ 2 = | 448 | 0 | 00 | |
448 | ÷ 2 = | 224 | 0 | 000 | |
224 | ÷ 2 = | 112 | 0 | 0000 | |
112 | ÷ 2 = | 56 | 0 | 00000 | |
56 | ÷ 2 = | 28 | 0 | 000000 | |
28 | ÷ 2 = | 14 | 0 | 0000000 | |
14 | ÷ 2 = | 7 | 0 | 00000000 | |
7 | ÷ 2 = | 3 | 1 | 100000000 | |
3 | ÷ 2 = | 1 | 1 | 1100000000 | |
1 | ÷ 2 = | 0 | 1 | 11100000000 | |
0 | done. |
Here is an example of using repeated division to convert 1792 decimal to octal:
Decimal Number | Operation | Quotient | Remainder | Octal Result | |
1792 | ÷ 8 = | 224 | 0 | 0 | |
224 | ÷ 8 = | 28 | 0 | 00 | |
28 | ÷ 8 = | 3 | 4 | 400 | |
3 | ÷ 8 = | 0 | 3 | 3400 | |
0 | done. |
Here is an example of using repeated division to convert 1792 decimal to hexadecimal:
Decimal Number | Operation | Quotient | Remainder | Hexadecimal Result | |
1792 | ÷ 16 = | 112 | 0 | 0 | |
112 | ÷ 16 = | 7 | 0 | 00 | |
7 | ÷ 16 = | 0 | 7 | 700 | |
0 | done. |
The only addition to the algorithm when converting from decimal to hexadecimal is that a table must be used to obtain the hexadecimal digit if the remainder is greater than decimal 9.
Decimal: | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
Hexadecimal: | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
Decimal: | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
Hexadecimal: | 8 | 9 | A | B | C | D | E | F |
The addition of letters can make for funny hexadecimal values. For example, 48879 decimal converted to hex is:
Decimal Number | Operation | Quotient | Remainder | Hexadecimal Result | |
48879 | ÷ 16 = | 3054 | 15 | F | |
3054 | ÷ 16 = | 190 | 14 | EF | |
190 | ÷ 16 = | 11 | 14 | EEF | |
11 | ÷ 16 = | 0 | 11 | BEEF | |
0 | done. |
Other fun hexadecimal numbers include: AD, BE, FAD, FADE, ADD, BED, BEE, BEAD, DEAF, FEE, ODD, BOD, DEAD, DEED, BABE, CAFE, C0FFEE, FED, FEED, FACE, BAD, F00D, and my initials DAC.
Now on to octal conversions...