8_1_5

WHAT: Carry out addition and subtraction in Binary

SMART START:

Count from 0 to 10 in binary in your head.

Extra Mile:

Write down the 2 times table in binary.

HOW:

ADDITION

Activity 1 - READ

Before you can add binary numbers together, you first need to learn how to count in binary.

The animation shows counting from 0 to 15 in Binary. Watch it carefully. Keep watching it until you spot the pattern.

Binary only has two digits, 1 and 0. When it runs out of digits it needs to move along to a new placeholder. This keeps repeating as we keep adding 1.

Activity 2 - READ

There are four golden rules for Binary Addition:

Rule 1 0 + 0 = 0 (0 + 0 = 0 in decimal)

Rule 2 0 + 1 = 1 (0 + 1 = 1 in decimal)

Rule 3 1 + 1 = 10 (1 + 1 = 2 in decimal)

Rule 4 1 +1 + 1 = 11 (1 + 1 + 1 = 3 in decimal)

Study the following animations to learn what happens when two small numbers are added together:

1 + 1 (1+1 = 2 in decimal)

1 + 10 (1 + 2 = 3 in decimal)

Activity 3

Try it yourself:

  • 1 + 11 = ?

  • 10 + 10 = ?

  • 11 + 10 = ?

  • 11 + 11 = ?

Remember the golden rules!

You can check your working by converting the numbers to decimal numbers and checking your maths.

Activity 4

If you were correct then try the examples on the worksheet below:

Binary Maths Questions (Google Sheet)

(self mark using http://www.calculator.net/binary-calculator.html )

SUBTRACTION

SMART START:

Count backwards 10 to 0 in binary in your head.

Activity 1 - READ

Subtraction also has some golden rules. Think back to when you first learnt how to subtract numbers in primary school. It is a little bit like that!

There are four golden rules for Binary Subtraction:

Rule 1 0 - 0 = 0 (0 - 0 = 0 in decimal)

Rule 2 1 - 1 = 0 (1 - 1 = 0 in decimal)

Rule 3 1 - 0 = 1 (1 - 0 = 1 in decimal)

Rule 4 0 - 1 = 1 (*requires borrowing)

1 - 1 = 0 (1 - 1 = 0 in decimal)

0100 - 0010 = 0010 (4 - 2 = 2 in decimal)

Activity 2

Try some yourself:

  • 11 - 11 = ?

  • 10 - 01 = ?

  • 111 - 1 = ?

(self mark using http://www.calculator.net/binary-calculator.html )

Activity 3

If you are starting to understand it now, try the worksheet below:

Binary Maths Question Subtract

CHECK:

EMBED:

This task is on Google Classroom! (for VIPS)

Create a binary maths test for another student in your class to try. You should create the question sheet and the answers. You can then swap question sheets and try each others out.

CLASSROOM IDEAS:

Re-enforce the golden rules for addition and subtraction. This will help the students complete the arithmetic quickly. This is best completed as a teacher led activity with lots of practice at trying different difficulty levels.