The document discusses binary numbers and how computers use the binary system to store information. It explains that binary uses only two digits, 0 and 1, to represent all data. Eight bits make up one byte of data, and bytes can be combined to larger units like kilobytes and megabytes. It provides examples of how to determine the decimal value of a binary number by adding up place values for each 1 digit from right to left.

1. Binary In 1854, British mathematician George Boole published a paper detailing a system of logic that would become known as Boolean algebra . His logical system proved instrumental in the development of the binary system, particularly in its implementation in electronic circuitry.

2. Binary A numbering systems that only uses two digits. 0 and 1 . Rather than a base ten that we are all familiar with. Computers use binary to store information in a digital format. Each digit ( 0 or 1 ) represents one bit Eight bits are equal to one byte.

3. Bit One Binary Digit abbreviation is “ b ” Can be thought of as one character Either a 1 or a 0

4. Byte Eight bits make up one byte Abbreviation “ B ” Combination of 1’s and 0’s Can be thought of as one character 11101010

5. kilobit 1024 bits Abbreviation “ Kb ”

6. kilobytes Represented by KB Slang “Kilo” Is equal to 1024 bytes 2 10

7. megabytes Represented by MB Slang “Meg” Is equal to 1,000000 bytes One million bytes 2 20

8. gigabyte Represented by GB Slang “Gig” Equal to 1,000,000,000 Bytes One Billion bytes 2 30

9. terabyte Represented by TB Slang “tera” Equal to 1,000,000,000,000 Bytes One Trillion bytes 2 40

10. petabyte Represented by PB Slang “peta” Equal to 1,000,000,000,000,000 Bytes One Thousand Trillion bytes 2 50

11. exabyte Represented by EB Slang “exa” Equal to 1,000,000,000,000,000,000 Bytes One Million Trillion bytes 2 60 All printed materialin the world would use about 5 Exabytes

12. Binary Think of Binary as light bulbs that are either ON or Off

13. Binary All eight of these Light bulbs would represent one byte One Light bulb represents one Bit

14. Binary Think of Binary as light bulbs that are either ON or Off 1 0 0 0 0 0 0 1

15. Binary Exercise

16. Binary Figuring Binary. Starting on the right going to the left The first digit will be 1 The second digit will be 2 The third digit will be 4 The fourth digit will be 8 The fifth digit will be 16 The sixth digit will be 32 The seventh digit will be 64 The eighth digit will be 128

17. Binary Base Ten numbers are tabulated Left to Right.

18. Binary Binary numbers are tabulated Right to Left.

19. Example 1 0000000 The 1 st – 7 th digit would be Off The Eighth digit would be On The first digit will be 1 0 The second digit will be 2 0 The third digit will be 4 0 The fourth digit will be 8 0 The fifth digit will be 16 0 The sixth digit will be 32 0 The seventh digit will be 64 0 The eighth digit will be 128 + 128 Add the bits The value of the number would be Total 128

20. Example 1 000000 1 The 1 st digit would be On The 2 nd – 7 th digit would be Off The Eighth digit would be On The first digit will be 1 1 The second digit will be 2 0 The third digit will be 4 0 The fourth digit will be 8 0 The fifth digit will be 16 0 The sixth digit will be 32 0 The seventh digit will be 64 0 The eighth digit will be 128 + 128 Add the bits The value of the number would be Total 129

21. Example 1 00000 11 The 1 st digit would be On The 2 nd digit would be On The 3 rd – 7 th digit would be Off The Eighth digit would be On The first digit will be 1 1 The second digit will be 2 2 The third digit will be 4 0 The fourth digit will be 8 0 The fifth digit will be 16 0 The sixth digit will be 32 0 The seventh digit will be 64 0 The eighth digit will be 128 + 128 Add the bits The value of the number would be Total 131

22. Example 1 0000 111 The 1 st- 3 rd digit would be On The 4 th – 7 th digit would be Off The Eighth digit would be On The first digit will be 1 1 The second digit will be 2 2 The third digit will be 4 4 The fourth digit will be 8 0 The fifth digit will be 16 0 The sixth digit will be 32 0 The seventh digit will be 64 0 The eighth digit will be 128 + 128 Add the bits The value of the number would be Total 135

23. Example 11 000 000 The 1 st- 6 th digit would be Off The 7 th digit would be On The 8 th digit would be On The first digit will be 1 0 The second digit will be 2 0 The third digit will be 4 0 The fourth digit will be 8 0 The fifth digit will be 16 0 The sixth digit will be 32 0 The seventh digit will be 64 64 The eighth digit will be 128 + 128 Add the bits The value of the number would be Total 192

24. Binary Think of Binary as light bulbs that are either ON or Off What is the value? 192 1 1 0 0 0 0 0 0

25. Example 11111111 The 1 st- 8 th digit would be On The first digit will be 1 1 The second digit will be 2 2 The third digit will be 4 4 The fourth digit will be 8 8 The fifth digit will be 16 16 The sixth digit will be 32 32 The seventh digit will be 64 64 The eighth digit will be 128 + 128 Add the bits The value of the number would be Total 255 1 1 0 0 0 0 0 0

26. Binary Think of Binary as light bulbs that are either ON or Off 1 1 1 1 1 1 1 1 What is the value? 255 128 64 32 16 8 4 2 1

27. Using Calculator to figure Binary Numbers First we would open Calculator Start/All Programs/Accessories/ Calculator From the Calculator go to View and down To SCIENTIFIC

28. Scientific

30. This is the Scientific Calculator The next thing we would need to do in select BIN for Binary

32. Next we would enter the Binary number For example 10000000

34. After entering the Binary number we would then select the Dec Radio Button

36. We now see the answer to the problem Is 128

38. Binary Think of Binary as light bulbs that are either ON or Off What is the value? 192 1 1 0 0 0 0 0 0