Part of Lesson Plan: B5- Life Without Thumbs- Counting like Computers (by eights)

Activity Overview / Details

On the board, begin counting in octal. Have the students count with you. 0,1,2,3,4,5,6,7,10,11,12,13— Stop and ask them what the number 13 in octal is in decimal. It would be 11 in decimal! Write the two number side by side, 13 and 11. How would a computer programmer know just by looking at one of these numbers what the actual amount was?

One way would be to add the notation mathematicians use- a subscript number after the number to indicate the base. For example, 13 ₈ would mean the number 13 counting in base 8 or octal. However, this is difficult to do in computer work since there is no easy way to create a subscript in a simple line of text like a computer would see, so computer programmers have come up with another way. They put a zero (which you would not normally begin a number with) and then a letter to indicate the most common types of numbering systems computers use. So if a number begins with 0b, like 0b1101, it means the number is binary. If it begins with a zero, like 0356, it probably is octal. To indicate hexadecimal, they begin the number with 0x, like 0x856a. Normal decimal numbers do not have the leading zero.

Add a zero before the number 13 to make it 013. Now can they tell which number is octal?