Numeral System
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 Numeral System - Base-2
Binary numbers uses only 0 and 1 digits.
B denotes binary prefix.
Examples:
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 Numeral System - Base-8
Octal numbers uses digits from 0..7.
Examples:
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 Numeral System - Base-10
Decimal numbers uses digits from 0..9.
These are the regular numbers that we use.
Example:
253810 = 2×103+5×102+3×101+8×100
Hexadecimal Numeral System - Base-16
Hex numbers uses digits from 0..9 and A..F.
H denotes hex prefix.
Examples:
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
Numeral systems conversion table
| 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 |