How to Read Binary the Easy Way
What is Binary?
We are all familiar with the base 10 decimal system in one form or another which is based on ten digits zero through nine.
This convenient system is based on the number of digits we have on our hands.
While it may work fine for us in our everyday needs, it doesn't work well for electronic devices such as computers.
Why Do We Need Binary?
Computers need binary because they can only read two states, on or off. In binary the "on" state is represented by a 1 and the "off" state is represented by a 0.
Binary is needed to represent numbers using only 1's and 0's.
Understanding Binary
For most mathematicians binary is usually quite easy to understand. The formula is simple, multiply each binary digit by two to the power of its place number. Easy right?
Okay maybe it's not that easy. Before fully understanding binary it may help to take a look at our normal base 10 number system.
If we were to look at the number 1058 we would break that number down into into separate columns 1's, 10's, 100's and 1000's. The number 1058 is 11000's, 0100's, 510's and 81's.
In binary it works the same way. Each column represents a value. However in this case we can only have a 1 or a 0 to work with before we have to move on to the next column.
The number on the left of a particular number represents double what the value of the number to the right of it.
Confused yet? To make this system easier to understand, it helps to look at it more graphically. We'll use the binary number 100101101 for an example.
Binary Example: 100101101 = 301
Value of Digit if = 1
 (256)
 (128)
 (64)
 (32)
 (16)
 (8)
 (4)
 (2)
 (1)


Binary number example
 1
 0
 0
 1
 0
 1
 1
 0
 1

Value of the binary digit
 256
 0
 0
 32
 0
 8
 4
 0
 1

n our more graphic example of the number 100101101, the number in the brackets shows the value of the digit if it were a 1 (0 always equals zero).
Notice how the number to the left of each number doubles the number on the right. 1,2,4,8,16,32,64,128,256,512,1024 and so forth. Those who are familiar with computer memory or processors will probably recognize these numbers.
As we look at the binary number example above, we added the value of the digit if it equaled a 1 and a 0 if it equaled a zero.
At this point we can simply add up all the numbers in the "Value of the binary digit" row and we get the answer. 256+32+8+4+1= 301
So the binary number 100101101 = 301
Do you Find Binary Confusing?
Another Example
Here is another example. In this case we will use the binary 10100.
Value of Digit if =1
 (16)
 (8)
 (4)
 (2)
 (1)


Binary Number Example
 1
 0
 1
 0
 0

Value of the Binary Digit
 16
 0
 4
 0
 0

In this example we get the following numbers: 16+0+4+0+0 = 20. In other words 10100 = 20
Amaze Your Friends
Amaze your friends by showing them you can count to 20 using Binary!
Decimal Number
 Binary Number


0
 0

1
 1

2
 10

3
 11

4
 100

5
 101

6
 110

7
 111

8
 1000

9
 1001

10
 1010

11
 1011

12
 1100

13
 1101

14
 1110

15
 1111

16
 10000

17
 10001

18
 10010

19
 10011

20
 10100

Converting Base 10 to Binary
Converting a conventional base 10 number to binary is a fairly easy process. Let's convert the number 274 to binary:
To get started it helps to represent each column with their corresponding binary values:
512
 256
 128
 64
 32
 16
 8
 4
 2
 1


Looking at the column values we want to find the number that is as close to the number we are after without going over. In this case the number is 256.
Now subtract 256 from 274. This gives us 18. Next we want to find the number that is closest to 18 without going over. That would be 16. We next want to subtract 16 from 18. That will leave us 2. Next we want to find the number closest to 2 without going over. That number is of course 2.
Adding 1's into the appropriate locations on the chart we can find the binary representation of 274.
512
 256
 128
 64
 32
 16
 8
 4
 2
 1


1
 0
 0
 0
 1
 0
 0
 1
 0

Having Fun Using Binary
If you would like to have some fun using binary with your friends here is a link to a great site that converts binary to text or text to binary. There's even a special message message just for you that after you decode it may seem somewhat familiar.
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