Understanding Binary and Base-10 Number Systems
Learn about the binary and base-10 number systems, where computers operate in binary with only 0s and 1s, while humans use the base-10 system with numbers 0-9. Discover how to create place value columns and count in both systems, and explore the connection between the two for a deeper understanding of numbers.
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Presentation Transcript
CS101 Learning Binary Learning Binary
What do you think when you see.. 101 One hundred and one What does a computer think when it sees 101? 5
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
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
Creating 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 , 1000000, 100000, 10000, 1000, 100, 10, 1 Base 2 , 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1
Exam Tip Many binary questions on the quiz will be much easier if you can create the base two columns up to the 256 column.
Counting to 10 in base 2 and base 10 Base 10 0 1 2 3 4 5 6 7 8 9 10 Base 2 0 1 10 11 100 101 110 111 1000 1001 1010
Knowledge Check 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
Knowledge Check In the base 2 number system what number is this 101? A) 3 B) 5 C) 8 D) 45
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
Knowledge Check Which base 2 number below is equal to the base 10 number 37? A) 0100101 B) 1000011 C) 0010110 D) 1010111 E) 0010001
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
Knowledge Check Which base 10 number below is equal to the base 2 number 101101? A) 4 B) 16 C) 45 D) 56 E) 256
