1. CS101 Learning Binary
Learning Binary

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

3. 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

4. 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.

5. 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

6. 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

7. 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
…, , , 10000, 1000, 100, 10, 1
Base 2
…, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1

8. Quiz Tip
Many binary questions on the quiz will be much easier if you can create the base two columns up to the 256 column.

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

10. 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

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

12. 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

13. iClicker Which base 2 number below is equal to the base 10 number 65?D) E)

14. 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

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