## Thursday, February 28, 2013

Octal numbers are numbers written in base 8. Hexadecimal numbers are numbers written in base 16.
 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

## Reasons for using octal and/or hexadecimal

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.

## Method

1- Starting at the right split the binary number into groups of four bits.

2- Convert each group of bits to hexadecimal.

## Worked question

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

## Method

1- For each hexadecimal digit write the four-digit binary equivalent.

2- Ignore any zeros at the left.

## Worked question

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.