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

10 types of people

TOPIC OVERVIEW (Test your Knowledge)

ADDING BINARY NUMBERS

This is a simple task when you understand the following rules:

adding binary 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

adding binary

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…

LESSON TASKS

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

2. Binary Numbers (Complete in Book)

3. Extra Task

1. Adding Binary Numbers

2. Adding Binary Numbers

3. Binary Numbers Past Exam Questions

HEXADECIMAL NUMBERS

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.

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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

LESSON TASKS

1. Hexadecimal Worksheet

2. Hexadecimal Numbers Past Exam Questions

GAMES

Cisco Binary Game

Binary-Hex Challenge

Purpose Games (Hexadecimal)