Part of Lesson Plan: B5- Life Without Thumbs- Counting like Computers (by eights)
Activity Overview / Details
Have the students take out a piece of paper and write their names in the top right corner. Have them label it “Octal Numbers Lab”.
Have them fold the page lengthwise into quarters. Then have them number in the first column to 25, move to the next column and number from 26-50 and so on until they reach 100.
Now tell them to begin counting in octal beside the number- 0,1,2,3,4,5,6,7,10,11,12- all the way to 100. Tell them to be sure to leave space after the octal number, as there will be one more number added later. When they reach 100 decimal, what number do they get octal? They should get 0144.
Write this question on the board—
“Why do computer programmers always mix up Halloween and Christmas?”
If they are having difficulty, have them circle the number pair 25-031 on their papers. If they still don’t get it, the joke is that decimal 25 and octal 31 are the same number- Dec.25 and Oct. 31, the dates of Christmas and Halloween!
For a little added humor, play the attached video from “Nightmare Before Christmas” where Jack Skellington from Halloween is trying to understand Christmas.
Now have the students write the same number in binary beside the octal number. So, for example, the number 25 would look like this: 25. 031 0b11001. Have them draw lines dividing the binary into groups of three bits each. So the binary equivalent of decimal 100 would be 1|100|100. Have them compare the groups of three bits with the octal number. Point out that every three binary bits can be represented as one octal number. In this case, 1=1, 100=4 and 100=4 for binary 0144. This is one of the reasons computer programmers find it easier to work in octal. Octal can be more easily translated back and forth to binary.