1. Starter Using the mini whiteboards record your answers: 1) Name 2 different Character Sets 2) Convert the Hex number 9E into denary 3) Convert the binary number 01110111 into Denary and Hex

2. Representation of Negative Numbers (Textbook Page 193)

3. Objectives Understand that negative whole numbers can be represented using the Sign & Magnitude method. Understand that negative whole numbers can be represented using the TWO’s Complement method.

4. Exam Questions on this Topic 1) Show how the number –7 is represented in two’s complement form using 8 bits. [1] Jan 2011 2) In a certain computer, integers are stored using sign/magnitude representation and 16 binary digits. The left hand bit is set to zero for a positive number. Find the integer represented by the binary number 1000000000001001 [1] Jun 2012 Where do you think you fall on the Progress Scale?

5. Assessment Objectives (Outcome) Grade E/D Standard: Be able to understand how to convert from negative denary numbers using the two methods and achieve more than 40% of the exam style question. Grade C/B Standard: Be able to understand and demonstrate how to convert negative denary numbers using the two methods and achieve 60% or more of the exam style question. Grade A Standard: Be able to understand, demonstrate and teach others independently how to negative denary numbers using the two methods and achieve 80% or more in the exam style questions.

6. Learning the Methods (30 Minutes) Working in pairs: Learn the method you have been given and make notes of the method. Put together 5 questions you could ask to test the learning using this method. Teach your method to your partner so that they know how to use this method. Partner to make notes of the method. Use your questions to test their understanding.

7. Adding Binary Numbers Example: Add the decimal numbers 12 and 10 in binary using the twos complement method: Step 1: Convert the decimal numbers to their equivalent twos complement binary number: 00001100 = 12 00001010 = 10 Step 2: Add them together in binary: (Remember 10 in binary is 2 in decimal) 0 0 0 0 1 1 0 0 = 12 0 0 0 0 1 0 1 0 = 10 01 10 1 Carry the one 1 000 = 22

8. Activity 1)Convert the decimal number -27 using the sign and magnitude method. 2) Convert the decimal number -27 using the twos complement method. 3) Show how the calculation 53 – 25 is actually 53 + - 25 using twos complement binary.

9. Activity - Answers 1)10011011 = -27 (S&M) 2) 00011011 = 27 = 11100101 = -27 (TC) 3) 00011001 = 25 11100111 = -25 (TC) + 00110101 = 53 -------------- (1) 00011100 = 28 (1) is overflow and doesn’t count 53 – 25 = 28 53 + -25 = 28

10. On-Line Assessment(30 Minutes) Go to http:\\m.socrative.com Enter room 307448 Complete quiz on your own

11. Stretch & Challenge Activity 1) Show how the number –7 is represented in two’s complement form using 8 bits. [1] Jan 2011 2) In a certain computer, integers are stored using sign/magnitude representation and 16 binary digits. The left hand bit is set to zero for a positive number. Find the integer represented by the binary number 1000000000001001 [1] Jun 2012 3) In other computers, integers are stored using two’s complement representation. Describe, using an example, how the two’s complement of a binary number is derived. [3] June 2012

12. Extra Work A teacher wants to teach her students how to convert negative numbers using the sign & magnitude and two’s complement methods. Using a software of your choice create a teaching aid for the teacher and ensure your teaching aid tests the students knowledge.

13. Assessment Objectives (Outcome) Grade E/D Standard: Be able to understand how to convert from negative denary numbers using the two methods and achieve more than 40% of the exam style question. Grade C/B Standard: Be able to understand and demonstrate how to convert negative denary numbers using the two methods and achieve 60% or more of the exam style question. Grade A Standard: Be able to understand, demonstrate and teach others independently how to negative denary numbers using the two methods and achieve 80% or more in the exam style questions.

14. Objectives Understand that negative whole numbers can be represented using the Sign & Magnitude method. Understand that negative whole numbers can be represented using the TWO’s Complement method.