| Decimal | Binary | Octal | Hexadecimal |
| (base 10) | (base 2) | (base 8) | (base 16) |
| 0 | 0000 | 0 | 0 |
| 1 | 0001 | 1 | 1 |
| 2 | 0010 | 2 | 2 |
| 3 | 0011 | 3 | 3 |
| 4 | 0100 | 4 | 4 |
| 5 | 0101 | 5 | 5 |
| 6 | 0110 | 6 | 6 |
| 7 | 0111 | 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 |
Fig 3 Conversion table for small numbers
Although they are stored in a computer in binary form, bit strings are often displayed by or entered into a computer in octal or hexadecimal form. This is because:
1- Binary strings are longer than their octal or hexadecimal equivalents. This means:
(a) Octal or hexadecimal strings do not take up much room when displayed.
(b) Binary strings take longer to type in.
2- Binary strings are difficult to recognize and remember.
3- As octal and hexadecimal are each based on a power of 2, they can be converted to and from binary easily.
1- Starting at the right split the binary number into groups of four bits.
2- Convert each group of bits to hexadecimal.
A location contains the value 1001101011 in binary.
How would this be displayed in hexadecimal?
|
| Comments | ||
| 10 | 0110 | 1011 | Starting at the right group into fours For each group write hexadecimal equivalent |
| 2 | 6 | B |
Answer 10011010112=26B16
1- For each hexadecimal digit write the four-digit binary equivalent.
2- Ignore any zeros at the left.
The address of a location is 2B6A in hexadecimal. What is it in binary?
| 2 | B | 6 | A | Comment |
| 0010 | 1011 | 0110 | 1010 | For each hexadecimal digit write the binary equivalent |
The address is 0010 1011 0110 1010
Notes:
1- In the example addresses may occupy 16 bits so the two 1s at the left were not discarded.
2 -The methods for converting between octal and binary are similar with each octal digit corresponding to three binary digits.
Labels: Computer