Teaching Computer Science: Day 11 - "1 + 1 = 10"

In this week’s lesson, I continued the theme of how data is stored in computers, this week focusing on binary addition.

Learning Objectives:

• add two 8‐bit binary integers and explain overflow errors which may occur
  

Lesson 1: Theory (Binary Addition)

Suggested time: 50 mins

Starter:

I started with a fun starter activity courtesy of Mark Ward via CAS called Binary Bingo. To download the activity, click here. 

Each student was given a bingo card and numbers were picked at random using a free random name selector (see Classroom Management Tools). The first student to get a full house was the winner.

Main:

I began by writing a simple sum (adding to denary numbers together) on the board:

I then asked for a volunteer to solve it (showing all working out).

Next, I introduced a simple binary sum:

I explained that adding binary numbers is exactly the same as adding denary numbers however, instead of carrying groups of ten, you carry groups of 2. I followed this by writing a couple more simple binary sums on the board and asked for volunteers to attempt to solve these.

Next I explained that when we add two 1s we need to carry over to the next column. I demonstrated this using the following sum:

I followed this by asking students to work out the following (explaining their working out):

Finally, I wrote the following binary sum on the board and asked the students to solve it. I then asked the students if they spotted the problem.

I explained that, if we only have 4 bits to store the result, there would be no room for the final carry – resulting in the wrong answer. I explained that when there isn’t room to store the resulting calculation, we get an error which we call overflow.

Finally, I gave students a series of binary addition challenges courtesy of Chris Barnard via CAS. You can download the worksheet and answer sheet here: Binary Addition Exercise 


Extension:

Students were directed to the following YouTube video explaining binary subtraction:

Plenary:

Students played the CISCO Binary Game: http://forums.cisco.com/CertCom/game/binary_game_page.htm    


Resources:

Useful resources:

Binary Calculator – http://gwydir.demon.co.uk/jo/numbers/binary/add.htm

Binary Arithmetic Task - http://www.allaboutcircuits.com/worksheets/bin_math.html

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Lesson 2: Raspberry Pi - Python Challenge

Suggested time: 50 mins

Main:

Students were instructed to setup their Raspberry Pis and to launch IDLE 3.

Students were then asked to attempt a series of introductory Python challenges courtesy of Tom Gilmour via CAS: http://community.computingatschool.org.uk/resources/332

Alternative:

Alternatively, if you do not have access to a set of Raspberry Pis, students can still complete the Python challenges:

To install Python for FREE, go to the python.org website and download a standard installation of the latest version of Python. This will provide you with everything you need.