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SECTION I-8: Counting in Bases 10, 2, and 16
Table Below demonstrated the relationship between all three Bases. Showed the sequence of numbers from 0 to 31 in decimal, along with the equivalent Binary and Hex numbers. In each base that when one more is added to the the highest digit, that digit becomes zero and a 1 is carried to the next-highest digit position. In decimal, 9 + 1 = 0 with a carry to the next-highest position. In Binary, 1 + 1 = 0 with a carry; similarly, in Hex, F + 1 = 0 with a carry.
Decimal | Binary | Hex |
---|---|---|
0 | 00000 | 0 |
1 | 00001 | 1 |
2 | 00010 | 2 |
3 | 00011 | 3 |
4 | 00100 | 4 |
5 | 00101 | 5 |
6 | 00110 | 6 |
7 | 00111 | 7 |
8 | 01000 | 8 |
9 | 01001 | 9 |
10 | 01010 | A |
11 | 01011 | B |
12 | 01100 | C |
13 | 01101 | D |
14 | 01110 | E |
15 | 01111 | F |
16 | 10000 | 10 |
17 | 10001 | 11 |
18 | 10010 | 12 |
19 | 10011 | 13 |
20 | 10100 | 14 |
21 | 10101 | 15 |
22 | 10110 | 16 |
23 | 10111 | 17 |
24 | 11000 | 18 |
25 | 11001 | 19 |
26 | 11010 | 1A |
27 | 11011 | 1B |
28 | 11100 | 1C |
29 | 11101 | 1D |
30 | 11110 | 1E |
31 | 11111 | 1F |