The hexadecimal system uses base 16. Thus, it has 16 possible digit symbols. It uses the digits 0 through 9 plus the letters A, B, C, D, E, and F as the 16 digit symbols.
| 163 | 162 | 161 | 160 | 16-1 | 16-2 | 16-3 | |
| =4096 | =256 | =16 | =1 | . | =1/16 | =1/256 | =1/4096 |
| Most Significant Digit | Hexadec. point | Least Significant Digit |
Hexadecimal to Decimal Conversion
eg. 2AF16 = 2 x (162) + 10 x (161) + 15 x (160) = 68710
Repeat Division: Convert decimal to hexadecimal
This method uses repeated division by 16. Eg. convert 37810 to
hexadecimal and binary:
| 378/16 | = 23+ remainder of 10 | A (Least Significant Bit) |
| 23/ 16 | = 1 + remainder of 7 | 7 |
| 1 / 16 | = 0 + remainder of 1 | 1 (Most Significant Bit) |
| Result | 37810 = | 17A8 |
| Convert to Binary | = 0001 0111 10102 = 0000 0001 0111 1010 (16 bits) |
Binary-To-Hexadecimal /
Hexadecimal-To-Binary Conversion
| Hexadecimal Digit | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Binary Equivalent | 0000 | 0001 | 0010 | 0011 | 0100 | 0101 | 0110 | 0111 |
| Hexadecimal Digit | 8 | 9 | A | B | C | D | E | F |
| Binary Equivalent | 1000 | 1001 | 1010 | 1011 | 1100 | 1101 | 1110 | 1111 |
Each Hexadecimal digit is represented by four bits of binary digit.
eg. 1011 0010 11112 = (1011) (0010) (1111)2 = B 2 F16
Octal-To-Hexadecimal /
Hexadecimal-To-Octal Conversion
1) Convert Octal (Hexadecimal) to Binary first.
2a) Regroup the binary number in 3 bits a group starts from the LSB if
Octal is required.
Go back to Section 2.3 if you are not sure how to group in Octal.
2b) Regroup the binary number in 4 bits a group from the LSB if
Hexadecimal is required.
eg. Convert 5A816 to Octal .
5A816 | = 0101 1010 1000 (Binary) |
| = 2 6 5 0 (Octal) |
