1. ©2010 Akula LLC, Jeremy R. Hertzberg, BS CMPE Binary Numbers Zeros and Ones http://commons.wikimedia.org/wiki/File:Wikipedia_in_binary.svg

2. ©2010 Akula LLC, Jeremy R. Hertzberg, BS CMPE Decimal or Base 10 1 2 3 4 56 7 8 9 10 Can you see a good reason for developing a counting system based on the number 10? http://commons.wikimedia.org/wiki/File:Lamh.JPG

3. ©2010 Akula LLC, Jeremy R. Hertzberg, BS CMPE In the decimal system, when you look at the number 1234, the numeral 4 is in the ONES place, 3 is in the TENS place, 2 is in the HUNDREDS place, and 1 is in the THOUSANDS place. Each place is 10 times bigger than the place to its right. 1000s 100s 10s 1s 1 2 3 4

4. ©2010 Akula LLC, Jeremy R. Hertzberg, BS CMPE Babylonian number system The ancient Babylonians used a number system based on the number 60. This is called sexigesimal or base 60. Instead of places for 1, 10, 100, 1000, etc., the Babylonians had places for 1, 60, 360, 21600, etc. They used a reed stylus to make marks on clay tablets. The numerals we use now hadn’t been invented yet.

5. ©2010 Akula LLC, Jeremy R. Hertzberg, BS CMPE http://math.ucr.edu/home/baez/diary/september_2006.html Babylonian numbers

6. ©2010 Akula LLC, Jeremy R. Hertzberg, BS CMPE Binary or Base 2 Computers use a system based on electrical switches which have two states, either on or off. This system is called binary or base 2

7. ©2010 Akula LLC, Jeremy R. Hertzberg, BS CMPE Binary only uses two numerals, 0 and 1. In computer terms, these are called bits. This is what binary counting looks like next to decimal counting: Binary Decimal 1 1 10 2 11 3 100 4 101 5 110 6 111 7 1000 8 1001 9 101010

8. ©2010 Akula LLC, Jeremy R. Hertzberg, BS CMPE In binary, when you look at the number 1011, the first numeral 1 on the right is in the ONES place, the second numeral 1is in the TWOS place, the 0 is in the FOURS place, and third 1 is in the EIGHTS place. Each place is 2 times bigger than the place to its right. 8s 4s 2s 1s 1 0 1 1

9. ©2010 Akula LLC, Jeremy R. Hertzberg, BS CMPE Converting Larger Binary Numbers to Decimal: 128s 64s 32s 16s 8s 4s 2s 1s 1 0 1 0 1 0 1 1 = 171 128+0+32+0 +8 +0 +2+1 = 171 1 1 1 0 0 0 1 = 113 64+32 +6+0 +0 +0+1 = 113 1 1 0 0 1 0 0 0 = 200 128+64+0 +0 +8 +0 +0+0 = 200

10. ©2010 Akula LLC, Jeremy R. Hertzberg, BS CMPE Binary joke There are only 10 types of people in the world: Those who understand binary, and those who don't.