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## Binary

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**Binary**Converting to and from decimal SW Abingdon and Witney College**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**Decimal positions**Eight thousand two hundred and fifty three SW Abingdon and Witney College**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**Binary positions**One eight, one four, no twos and one unit That makes thirteen SW Abingdon and Witney College**Counting in binary and decimal**SW Abingdon and Witney College**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**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**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**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**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**Convert binary to decimal**Convert 11001010 binary to decimal Write in the binary digits under their values SW Abingdon and Witney College**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**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**One for you to try**• Convert 10010101 from binary (base 2) to decimal (base 10) SW Abingdon and Witney College**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**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**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**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**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**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**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**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**Convert decimal to binary**185 decimal is 10111001 binary SW Abingdon and Witney College**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**One for you to try**• Convert 248 from decimal to binary • Check your answer SW Abingdon and Witney College**End**SW Abingdon and Witney College