The Binary Number System

6th grade math

What is binary?

• The number system we use is decimal, based on the number 10

• The binary system is instead based on the number 2

• So, if the decimal system is based on 10 and we use the numbers 0-9, what numbers do you think we can use in the binary system that is based on 2?

Terminology

• Bit – one digit in the binary number system• Nibble – 4 digits (or significant digits) in the

binary system– Example: 0101

• Byte – 8 digits (or significant digits) in the binary system– Example: 01010101

Why use binary?

• Electronics, especially computers, only really know on and off (represented by 1 and 0)

• So for these, everything stored is actually stored in a set 0’s and 1’s

• Although we do not write computer programs in binary, what we write is turned into the 0’s and 1’s the computer (or other electronic device) needs to understand

So how does it work?

• So if we only have 0 and 1 to work with, how do we represent other numbers?

• In decimal, the place value is in powers of 10 and as you move left in a number, the place value is a higher power of 10:– Example: 5,321 =

• Binary works in the same way, but with powers of 2:– Example: 01101 =

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5 ×103 + 3 ×102 +2 ×101 +1×100

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0 × 24 +1× 23 +1× 22 +0 × 21 +1× 20

Videos to watch

• The following help to explain how this works (watch all):– This first video introduces the concepts of different number

systems:• http://www.youtube.com/user/MyWhyU?v=5sS7w-CMHkU&feature

=pyv

– This second video introduces the concept of binary and how it works• http://www.youtube.com/watch?v=b6vHZ95XDwU

– This third video focuses on binary counting:• http://www.youtube.com/watch?v=Pz7dLWvi2w0

– This last video talks more on how to translate decimal numbers into binary:• http://www.youtube.com/watch?v=ETsfylK7kzM

Binary <-> Decimal

• The first thing to master is the ability to translate numbers from binary into decimal and from decimal to binary.

• To go from decimal to binary:– There are 2 methods:

• Continually dividing by 2• Compare with powers of 2 and subtract

– This website explains both with great pictures and examples:• http://www.wikihow.com/Convert-from-Decimal-to-Bina

ry

Practice translating from decimal to binary

• Start by counting from 0 to 50 in binary on a piece of paper .– Note patterns that you see

• Now see if you can translate these into binary:127 65 378 95 199

85 101 76 222 1024

189 864 432 765 57

1000 543 1022 678 555

Binary <-> Decimal

• To go from binary to decimal, we basically can reverse either of the methods we used to get into binary:

• Continually doubling• Positional notation

• This website explains both with great pictures and examples:– http://www.wikihow.com/Convert-from-Binary-to-

Decimal

Practice translating from binary to decimal

• Using which ever method you prefer, see if you can translate the following binary numbers into decimal:

1101010 100 1010 10101 1111

110 101010 11110 1010010 1110001

100010000 110100 11000011 1101110 11111111

Some online games to practice

• Try your hand at some of these to make sure you can translate back and forth between decimal and binary

• Both translations are tested here:– http://forums.cisco.com/CertCom/game/binary_game_

page.htm– http://people.sinclair.edu/nickreeder/Flash/binDec.htm

• Binary to decimal: http://cis.msjc.edu/courses/core%5Fcourses/csis202/lessons/BinaryToDecimal/

• Decimal to binary:http://cis.msjc.edu/courses/core%5Fcourses/csis202/lessons/DecimalToBinary/

Work to do to complete this unit

• Page 8 – decimal to binary translations• Page 10 – binary to decimal translations• Play at least 2 online games on translating and

fill in the following:– I played___________ game at this

website_____________________________– I played___________ game at this

website_____________________________

In my own words• Explain how you know how to translate from

decimal to binary (use an example):

• Explain how you know how to translate from binary to decimal (use an example):

Things to notice

• If the right most bit is 0, the number is_______ and if it is 1, the number is ______.

• The largest 4 bit number that can be represented in binary is ________.

• The largest 8 bit number that can be represented in binary is ________.

• Name one other thing you notice about binary numbers___________________________________________________________________.