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Binary

Binary. Converting to and from decimal. Decimal. We normally use the decimal (denary) system, also called base 10 There are 10 different symbols (digits) 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 To count higher than nine we re-use the symbols by putting them in columns

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Binary

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  1. Binary Converting to and from decimal SW Abingdon and Witney College

  2. Decimal • We normally use the decimal (denary) system, also called base 10 • There are 10 different symbols (digits) • 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 • To count higher than nine we re-use the symbols by putting them in columns • The value of a symbol depends on its position SW Abingdon and Witney College

  3. Decimal positions Eight thousand two hundred and fifty three SW Abingdon and Witney College

  4. Binary • Computers use the binary system, also called base 2 • There are two different symbols (digits) • 0, 1 • To count higher than one we re-use the symbols by putting them in columns • The value of a symbol depends on its position SW Abingdon and Witney College

  5. Binary positions One eight, one four, no twos and one unit That makes thirteen SW Abingdon and Witney College

  6. Counting in binary and decimal SW Abingdon and Witney College

  7. Why do computers use binary? • Computer components that store or handle data are often two-state devices • This is like a switch that can be on or off • A memory unit could exist in two voltage states, high or low • A voltage on a cable could be high or low • A light could be on or off • Two states can be coded by binary 0 and 1 SW Abingdon and Witney College

  8. Why am I learning about binary? • You will learn about IP addresses and how to split up a network into subnets • You need to work out subnet addresses and workstation addresses • For this you need to use binary SW Abingdon and Witney College

  9. Bytes or octets • We often handle binary digits (bits) in groups of eight • Sometimes these groups are called bytes • Sometimes they are called octets • We shall often be calling them octets • Examples of octets: 00101101 10110010 SW Abingdon and Witney College

  10. Coding data into binary • Decimal numbers can be converted into binary numbers • Characters (letters, punctuation, digits) can be coded using ASCII or EBCDIC • Graphics, sounds and videos have several different and complicated methods for coding them • Program instructions are coded in a machine code that depends on the type of processor SW Abingdon and Witney College

  11. ACSII • American Standard Code for Information Interchange used for our alphabet • Uses 8 bits (one byte/octet) for each character • 7 bits for the basic character and one bit for error checking • Chinese, Arabic and some other languages require 16 bits (2 bytes) for each character – they use Unicode, related to ASCII SW Abingdon and Witney College

  12. Convert binary to decimal Convert 11001010 binary to decimal Write in the binary digits under their values SW Abingdon and Witney College

  13. Convert binary to decimal Convert 11001010 binary to decimal Write in the binary digits under their values Next write in the value for each binary 1 digit SW Abingdon and Witney College

  14. Convert binary to decimal Convert 11001010 binary to decimal Write in the binary digits under their values Next write in the value for each binary 1 digit Add up the values 128 + 64 + 8 + 2 = 202 SW Abingdon and Witney College

  15. One for you to try • Convert 10010101 from binary (base 2) to decimal (base 10) SW Abingdon and Witney College

  16. Convert decimal to binary Convert 185 decimal to binary Can you take 128 from 185? Yes. Put 1 under 128 What is left? 185-128 = 57 SW Abingdon and Witney College

  17. Convert decimal to binary Converting 185: we have 57 left Can you take 64 from 57? No. Put 0 under 64 What is left? Still 57 SW Abingdon and Witney College

  18. Convert decimal to binary Converting 185: we have 57 left Can you take 32 from 57? Yes. Put 1 under 32 What is left? 57 – 32 = 25 SW Abingdon and Witney College

  19. Convert decimal to binary Converting 185: we have 25 left Can you take 16 from 25? Yes. Put 1 under 16 What is left? 25 – 16 = 9 SW Abingdon and Witney College

  20. Convert decimal to binary Converting 185: we have 9 left Can you take 8 from 9? Yes. Put 1 under 8 What is left? 9 – 8 = 1 SW Abingdon and Witney College

  21. Convert decimal to binary Converting 185: we have 1 left Can you take 4 from 1? No. Put 0 under 4 What is left? Still 1 SW Abingdon and Witney College

  22. Convert decimal to binary Converting 185: we have 1 left Can you take 2 from 1? No. Put 0 under 2 What is left? Still 1 SW Abingdon and Witney College

  23. Convert decimal to binary Converting 185: we have 1 left Can you take 1 from 1? Yes. Put 1 under 1 What is left? Nothing. Finished. SW Abingdon and Witney College

  24. Convert decimal to binary 185 decimal is 10111001 binary SW Abingdon and Witney College

  25. Convert decimal to binary Check: write in the values of the1 digits and add them up 128 + 32 + 16 + 8 + 1 = 185 That’s the number we started with. It’s correct. SW Abingdon and Witney College

  26. One for you to try • Convert 248 from decimal to binary • Check your answer SW Abingdon and Witney College

  27. End SW Abingdon and Witney College

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