CS101 Learning Binary Learning Binary

What do you think when you see One hundred and one What does a computer think when it sees 101? 5

You are a base 10 creature You have learned the base 10 number system. The base 10 number system uses the numbers 0-9, or 10 total numbers.

Review base 10 number system Can only use numbers 0-9 in base ten system –10 different numbers allowed in a column in a base 10 system Columns have place value –You start with the one’s column –To find the next column to the left multiply the current column by 10. –…, thousands, hundreds, tens, ones

Good News All the base ten number system concepts you have learned can be used to learn the the base 2, or binary number system Except for: You only get to use 2 numbers in base two instead of the 10 numbers in base ten

Computers are base 2 creatures Computers can only use 0’s and 1’s. –Because their processors are made up of switches. The base 2 number system uses the numbers 0-1, or 2 total numbers. Binary means 2. Therefore, computers use the base 2, or binary number system

Creating base 2 place value columns Columns have place value –You start with the 1’s column –To find the next column to the left multiply the current column by the amount of numbers allowed in the base system. Base 10 …, , , 10000, 1000, 100, 10, 1 Base 2 …, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1

Quiz Tip Many binary questions on the quiz will be much easier if you can create the base two columns.

Counting to 10 in base 2 and base 10 Base 10Base

iClicker What number is this 11? –A) Eleven –B) Three –C) I do not know until you tell me the base –D) None of the above

iClicker How would you write the value of eleven in base two? –A) 11 –B) 0011 –C) 1100 –D) 1011 –E) 1111

Now that you know base 2, you can convert numbers between base 2 and base 10

Converting base 10 number to base 2 number Write down your base 10 number Write down your base 2 columns –Keep going until the base 2 column number is larger than the base 10 number Find biggest base 2 column that is equal to or smaller than base 10 number Add one set to that base 2 column and subtract the amount of the base 2 column from base 10 number Find the next biggest base 2 column that is equal to or smaller than the remaining base 10 number. –If you skip over any base two columns place zeros in them When you find the next base 2 column that is equal to or less then the remaining base 10 number add one set to that base 2 column and subtract the amount of the base 2 column from the remaining base 10 number. Keep repeating process until the base 10 number is down to zero. Place zeros in any remaining base 2 columns

iClicker Which base 2 number below is equal to the base 10 number 65? –A) –B) –C) –D) –E)

Converting base 2 number to base 10 number Write down your base 2 number Write down your base 2 columns on top of the base 2 number Determine which columns have a set on one in them and write down each column’s value as a base 10 addition problem Add up the values of your columns and you have your base 10 number

iClicker Which base 10 number below is equal to the base 2 number ? –A) 4 –B) 16 –C) 45 –D) 56 –E) 256

Using your base 2 knowledge (and practice for quiz) ary_game_page.htmhttp://forums.cisco.com/CertCom/game/bin ary_game_page.htm