You should be able to…

• Convert positive denary whole numbers (0-255) into 8-bit binary numbers and vice versa
• Add two 8-bit binary integers and explain overflow errors which may occur
• Convert positive denary whole numbers (0-255) into 2-digit hexadecimal numbers and vice versa
• Convert between binary and hexadecimal equivalents of the same number
• Explain the use of hexadecimal numbers to represent binary numbers

BINARY NUMBERS This is a simple task when you understand the following rules: You first need to write your binary numbers as follows:

1 0 1 0 1 0 1 1

1 0 1 0 1 0 1 0

You then need to remember that 0 and 0 make 0, 0 and 1 make 1, 1 and 0 make 1, 1 and 1 make 10 (resulting in a carry) and finally 1 and 1 and 1 make 11 (also resulting in a carry).

Example This is a 4 bit example above. In your exam you will be add 8 bit binary numbers together and show your working. If the addition results in an answer greater than 8 bit, eg 9 bit, then you should state that this would result in an ‘Overflow Error’ as the result cannot be stored in 8 bit. Watch the Psy video above to see how this idea resulted in Youtube crashing…

1. Binary Tasks 1, 2 , 3 (Complete On Screen)

2. Binary Numbers (Complete in Book)

3. Binary Numbers Past Exam Questions

TOPIC OVERVIEW

When given an 8 bit Binary number to convert into Hex you must first split it into two Nibbles (4 bit). Each Nibble should then be converted into a Decimal value and then finally into Hex using the table below. You don’t need to remember the entire table but just that Hex starts at 0 and count to 9 and then changes to letters, counting from A to F. Example 1

So…

1 1 1 1 1 1 1 1

becomes…

1 1 1 1        1 1 1 1

15               15

and in Hex…

FF

Example 2

So…

1 0 0 0 1 1 1 0

becomes…

1 0 0 0        1 1 1 0

8               14

and in Hex…

8E

WHY USE HEX?

• Binary produces longer strings than Hex
• Hex is easier to work with than Binary
• Hex can be easily converted to/from Binary (1 Hex digit per nibble)
• Hex is less susceptible to errors