1. Number systems Visualizing Decimal and Binary

2. We count in base 10 because people started by counting on their fingers Base 10 is a number system that uses 10 digits: 0-9 All of our numbers are made with these 10 digits: 532,699 4,887,012 956 14 60,044,117,005

3. How many fingers do you see? Did you have to count them all? (I hope not) How did you know there were 21? We count how many groups of 10, and then add the single fingers. 2 groups of 10 and 1 extra finger.

4. Numbers are easy to read because of place value 2,514 The ones place has the lowest value and is on the right. Each place has a value that is 10 times greater than the one to the right of it. Ones Tens Hundreds Thousands… etc.

5. To find the value of a number, multiply each digit times its place value. 3 hundreds 4 tens 7 ones 347

6. To write the number Three thousand Five hundred… Put a 3 in the thousands place and a 5 in the hundreds place. Which is correct? a) 35 b) 350 c) 0035 d) 3050 e) 3500 f) 35000 e) But Why ?? Because the PLACE where a number appears determines its value.

7. Binary is a number system with only 2 digits This works for things like:  Light bulbs or switches that are either on or off  Digital computers that store information using many on/off switches. Zero and One 100110111001011100110111001011 100110111001011100110111001011

8. Binary Numbers are also easy to read because of place value 1011 The ones place has the lowest value and is on the right. Each place has a value that is 2 times greater than the one to the right of it. Ones Twos Fours Eights… etc.

9. It’s easy to see that each place has twice the number of the one to it’s right. What will be the place value of the number to the left of 16? Hopefully you said 32. It’s fairly easy to double numbers. 1 2 4816

10. To show a number in binary, write a 1 if the card is showing, write a zero if the card is not showing. 001 = 1 010 = 2 011 = 3 100 = 4

11. What number is this?4+1 =5 How is 5 written in binary? 00101 There is nothing in the 16’s place There is nothing in the 8’s place There is 1 four There is nothing in the 2’s place There is 1 one SO, the answer is 00101 Or, since extra zeros on the left don’t count 101

12. Which cards are needed to make the number 12? 8 + 4 = 12 01100 What is the binary number for 12? 01100 Or 1100

13. Which cards are needed to make the number 27? 16 + 8 + 2 + 1 = 27 11011 What is the binary number for 27? 11011

14. In conclusion: Decimal is our ordinary base 10 number system using the digits 0-9 Binary is the base 2 number system using only the digits 0-1 All number systems have place value that determines the value of the digit in each place.