Peter Crawley

Don’t worry, by the end of class this will make sense.

Our number system We operate on a base 10 number system (we don’t

often refer to it as this because we use it all the time.

We have ten single digit numbers available to us

0,1,2,3,4,5,6,7,8,9

We can write all numbers in using a combination of these numerals

Counting When we count from zero to 9 we can use our numerals

To go past 9 we need to begin combining our numbers

1 represents the number of tens we have

0 represents the number of ones we have

The result is 10

We go through our numerals until we need another ten, so we change the 1 to a 2 and reset the ones to 0 to get 20

This pattern continues until we need a new digit (the hundreds)

Think of 100 as one hundreds unit, zero tens unit and zero ones unit

The Binary System The prefix bi means two (bicycle, bifold, etc.)

The binary system has two numerals (0 and 1)

The system works the same way as the base 10

0 means zero ones

1 means one one

We are now out of digits so we must add a new place, just like we added a new column for the tens, we now must add one for the twos (since there is no 2 in the system)

The Binary System So the next number would be 10, or one two and zero

ones (2 in our system)

Remember the saying “there are only 10 types of people in the world?”

The next would be 11, or one two and one ones (3 in our system)

We now must add a new place holder for the next number (the fours) and reset the others

100 would be 4 in our system (one four, zero twos and zero ones)

Placeholders In our system the places go up by multiplying by tens

You have your ones place, your tens place (1x10), your hundreds place (10x10), your thousands place (100x10),…)

In the binary system, the places go up by multiplying by 2

You still start with your ones place, then you have your twos place (2x1), your fours place (2x2), your eights place (4x2), your sixteens place (8x2)…

Writing Numbers in the Binary System Try writing the following numbers in binary

5

101 (1 four, 0 twos, and 1 one)

23

10111 (1 sixteen, 0 eights, 1 four, 1 two, 1 one)

153

10011001 (1 one hundred twenty eight, 0 sixty fours, 0 thirty twos, 1 sixteen, 1 eight, 0 fours, 0 twos, 1 one)

Writing Binary Numbers in Base 10 1010

10 (1 eight, 0 fours, 1 twos, 0 ones)

101101

45 (1 thirty two, 0 sixteens, 1 eight, 1 four, 0 twos, 1 one)

1011011

91 (1 sixty four, 0 thirty two, 1 sixteen, 1 eight, 0 fours, 1 two, 1 one)

Uses of the Binary Number System Binary is used in

computers and most programmable machines Electrical circuits can be

switch only to off and an

This translates to 1 and 0 in the binary system

Different combinations of off and on circuits communicate different things to a computer

Computers What you see on your

computer is really billions of pieces of information encoded in the binary number system

The computer decodes this information and changes it into the pictures and words you read on your screen

References http://www.xenvideo.com/category/interesting/page/

2/

http://www.zazzle.com/binary_poster-228033932120532793

http://bestuff.com/stuff/there-are-only-10-types-of-people-in-the-world-those-who-understand-binary-and-those-who-dont