b=16 {value of A=10, B=11, C=12, D=13, E=14, F=15}
(A0F) 16
= A * 162 + 0 *161 + F *160
= 10 * 162 + 0 *161 + 15 *160
=2560 + 15
= (2575) 10
Similarly 11.116 = 1 x (161) + 1 x (160) + 1 x (16-1) = 17.062510
12.316 = 1 x (161) + 2 x (160) + 3 x (16-1) = 18.187510
The weights of the corresponding bits for hexadecimal system are as
| 164 | 163 | 162 | 161 | 160 | . | 16-1 | 16-2 |
| 65536 | 4096 | 256 | 16 | 1 | . | 0.125 | 0.015625 |
| MSB | Decimal point |
Corresponding equivalents of decimal 0-15 in Binary, octal & hexadecimal system
Decimal Binary Octal Hexadecimal
0 0000 00 0
1 0001 01 1
2 0010 02 2
3 0011 03 3
4 0100 04 4
5 0101 05 5
6 0110 06 6
7 0111 07 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
This article has broadened my horizons to a whole new perspective; thank you.