3. Our number system We operate on a base 10 number system (we don’t often refer to it as this because we use it all the time. We have ten single digit numbers available to us 0,1,2,3,4,5,6,7,8,9 We can write all numbers in using a combination of these numerals
4. Counting When we count from zero to 9 we can use our numerals To go past 9 we need to begin combining our numbers 1 represents the number of tens we have 0 represents the number of ones we have The result is 10 We go through our numerals until we need another ten, so we change the 1 to a 2 and reset the ones to 0 to get 20 This pattern continues until we need a new digit (the hundreds) Think of 100 as one hundreds unit, zero tens unit and zero ones unit
5. The Binary System The prefix bi means two (bicycle, bifold, etc.) The binary system has two numerals (0 and 1) The system works the same way as the base 10 0 means zero ones 1 means one one We are now out of digits so we must add a new place, just like we added a new column for the tens, we now must add one for the twos (since there is no 2 in the system)
6. The Binary System So the next number would be 10, or one two and zero ones (2 in our system) Remember the saying “there are only 10 types of people in the world?” The next would be 11, or one two and one ones (3 in our system) We now must add a new place holder for the next number (the fours) and reset the others 100 would be 4 in our system (one four, zero twos and zero ones)
7. Placeholders In our system the places go up by multiplying by tens You have your ones place, your tens place (1x10), your hundreds place (10x10), your thousands place (100x10),…) In the binary system, the places go up by multiplying by 2 You still start with your ones place, then you have your twos place (2x1), your fours place (2x2), your eights place (4x2), your sixteens place (8x2)…
8. Writing Numbers in the Binary System Try writing the following numbers in binary 5 101 (1 four, 0 twos, and 1 one) 23 10111 (1 sixteen, 0 eights, 1 four, 1 two, 1 one) 153 10011001 (1 one hundred twenty eight, 0 sixty fours, 0 thirty twos, 1 sixteen, 1 eight, 0 fours, 0 twos, 1 one)
10. Uses of the Binary Number System Binary is used in computers and most programmable machines Electrical circuits can be switch only to off and an This translates to 1 and 0 in the binary system Different combinations of off and on circuits communicate different things to a computer
11. Computers What you see on your computer is really billions of pieces of information encoded in the binary number system The computer decodes this information and changes it into the pictures and words you read on your screen
