This lesson is a continuation of the lessons covered in Year 9 about Number Systems: Lesson 1 about different number systems and Lesson 2 about conversions between binary, decimal and hexadecimal.

Step 1:  follow the detailed lesson plan no 3., available in the resources section, to learn the rules for bits addition.

Step 2: view the video of binary addition.

Step 3: work out binary addition worksheets no. 1 and no. 2 available in the resources section.

Note: the answers are provided on the second page but try them out yourself first!

Now that you excel in binary addition, how do you think computers store negative numbers?

Introductory Note: Computers represent negative numbers using the Two’s Complement Method. For example, an 8 bit binary two’s complement representation can only store decimal numbers from -128 to +127. 

To convert a negative decimal number to binary:

1. find its positive binary equivalent,
2. invert the bits (1 becomes 0 and 0 becomes 1); the so-called One’s Complement representation, and
3. finally add 1; the so-called Two’s Complement representation.

Step 4: open the Two’s complement worksheet no. 3 available in the resources section.

Step 5:  work out Exercise 1: represent these numbers in 8 bit Two’s complement representation.

Note:  the most significant bit (MSB) in Two’s Complement becomes negative (in our case the 8th bit has a value of -128). This can help you to check that your working is correct. After completing the first exercise, you can check your answers by scrolling further down the worksheet. Hey, but I insist that you need to try them out on your own first!

Finally you need to understand how to carry out binary subtraction using the Two’s complement representation.

Step 6: follow the example (120 -36) on the detailed lesson plan. This can be worked out by working 120 + (-36).

• Did you try the online self test by following the web link provided?
• What happens if you need to subtract two negative numbers?
• What happens if the answer is greater that 127 or smaller than -128?

Step 7:  find out by working exercise 2 from the same worksheet (no. 3).

Well Done, you finished this lesson, it’s time to check next lesson about Binary Multiplication & Division