b - numeral system base
dn - the n-th digit
n - can start from negative number if the number has a fraction part.
N+1 - the number of digits
Binary numbers uses only 0 and 1 digits.
B denotes binary prefix.
101012 = 10101B = 1×24+0×23+1×22+0×21+1×20 = 16+4+1= 21
101112 = 10111B = 1×24+0×23+1×22+1×21+1×20 = 16+4+2+1= 23
1000112 = 100011B = 1×25+0×24+0×23+0×22+1×21+1×20 =32+2+1= 35
Octal numbers uses digits from 0..7.
278 = 2×81+7×80 = 16+7 = 23
308 = 3×81+0×80 = 24
43078 = 4×83+3×82+0×81+7×80= 2247
Decimal numbers uses digits from 0..9.
These are the regular numbers that we use.
253810 = 2×103+5×102+3×101+8×100
Hex numbers uses digits from 0..9 and A..F.
H denotes hex prefix.
2816 = 28H = 2×161+8×160 = 40
2F16 = 2FH = 2×161+15×160 = 47
BC1216 = BC12H = 11×163+12×162+1×161+2×160= 48146
Decimal
Base-10 |
Binary Base-2 |
Octal Base-8 |
Hexadecimal Base-16 |
---|---|---|---|
0 | 0 | 0 | 0 |
1 | 1 | 1 | 1 |
2 | 10 | 2 | 2 |
3 | 11 | 3 | 3 |
4 | 100 | 4 | 4 |
5 | 101 | 5 | 5 |
6 | 110 | 6 | 6 |
7 | 111 | 7 | 7 |
8 | 1000 | 10 | 8 |
9 | 1001 | 11 | 9 |
10 | 1010 | 12 | A |
11 | 1011 | 13 | B |
12 | 1100 | 14 | C |
13 | 1101 | 15 | D |
14 | 1110 | 16 | E |
15 | 1111 | 17 | F |
16 | 10000 | 20 | 10 |
17 | 10001 | 21 | 11 |
18 | 10010 | 22 | 12 |
19 | 10011 | 23 | 13 |
20 | 10100 | 24 | 14 |
21 | 10101 | 25 | 15 |
22 | 10110 | 26 | 16 |
23 | 10111 | 27 | 17 |
24 | 11000 | 30 | 18 |
25 | 11001 | 31 | 19 |
26 | 11010 | 32 | 1A |
27 | 11011 | 33 | 1B |
28 | 11100 | 34 | 1C |
29 | 11101 | 35 | 1D |
30 | 11110 | 36 | 1E |
31 | 11111 | 37 | 1F |
32 | 100000 | 40 | 20 |