The Human Binary Calculator: Investigating Positional Notation

Student Worksheet: name:______

In Show Math, you saw that the digits of Pi could be converted from the 10 digit number system regularly used, to the binary number system. In this activity you will learn more about this number system and become a human binary calculator with your group.

1. What is the difference between writing 25 and 52? Why is there a difference? Relate this to the importance of position when writing numbers. The Babylonian number system

The decimal number system is a number system with base ten, 2. In binary the order of the 1’s and 0’s are significant. Practice this means that there are ten converting a couple numbers from decimal to binary. digits used (0-9) and that each a)32 position to the left represents b)6 an increase by a power of 10. c)9 The binary number is a num- d)21 ber system with base 2, because e)3.5 there are two digits used (0,1) f)2.3125 and each position to the left rep- resents an increase by a power 3. Convert from binary to decimal. of 2. The Babylonians had a a)10101 number system of base 60. This b)1100 means that they had 60 different c)1 symbols used as their digits. To d)11.01 this day, we are not quite sure e)11.101 why the Babylonians used this f)0 are their number system, how- ever we think it is because 60 4. Why do you think the common system of numbers used today is the has many factors, in fact it is the decimal system? smallest number divisible by all the numbers 1-6. Can you think of anything in our world that uses base 60? Has the Babylo- nian number legacy lived on?