UNDERSTANDING BINARY NUMBERS
Most of us are used to representing numbers with ten digits, 0-9. This is called a base ten number system. Binary is a base two number system. This means there are only two digits that are used, ones and zeros, yet you can still write any number in binary. When counting in binary, every digit from the left is worth double the previous digit, here is an example:
| Value | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|
| Place | 5th digit | 4th digit | 3rd digit | 2nd digit | 1st digit |
The value of each digit is included in a number if in that place is a one, however if a zero is in that place the value of that number is not included. Using this you can see that if I were to write 01010 it would be equivalent to writing the number 10 because I am using the eights place and the twos place, 8+2=10.
| Value | 16 | 8 | 4 | 2 | 1 |
|---|---|---|---|---|---|
| Binary Number | 0 | 1 | 0 | 1 | 0 |
| Numbers Included in Binary Number | 0 | 8 | 0 | 2 | 0 |
Here are some more examples of how to write different numbers in binary:
| Number | Representation in Binary |
|---|---|
| One | 00001 |
| Two | 00010 |
| Three | 00011 |
| Four | 00100 |
| Five | 00101 |
| Six | 00110 |
| Seven | 00111 |
| Eight | 01000 |
| Nine | 01001 |
| Ten | 01010 |
| Eleven | 01011 |
| Twelve | 01100 |
| Thirteen | 01101 |
| Fourteen | 01110 |
| Fifteen | 01111 |
| Sixteen | 10000 |
HOW CHARACTERS ARE REPRESENTED IN BINARY
Using the first 8 digits in binary you can create numbers 0 through 255. There are also exactly 255 symbols you can type on he computer, including letters, numbers, punctuation marks, and more. Every binary number 1-255 represents its own symbol. Here is a website that lists all the symbols that can be represented with binary.
HOW BLACK AND WHITE IMAGES ARE REPRESENTED IN BINARY
Black and white images can be represented in binary by simply identifying which pixels in each row are on, and which are off. Every pixel in an image is either on or off. To represent this in binary ones are on and zeros are off. To find what pixels are on in a row you can count the number of pixels that are off in a row and then how many are on. So if an image had a row that looked like this: 000110, it could be represented by writing 3,2 in binary because there are three pixels that are off on the left fallowed by two pixels that are on.
HOW COLORED IMAGES ARE REPRESENTED IN BINARY
Colored images can be represented in binary almost the same as black and white images. When finding the color of the pixel, 0 still represents white, or off, but 1 and every other number in binary has its own color assigned to it. For example 01 (or 1) is blue, 10 (or 2) is green, and 11 (or 3) is red.
HOW AUDIO IS REPRESENTED IN BINARY
Audio can be represented in binary by using a microphone that can convert sound waves into voltages. Then the voltages can be checked at regular intervals and the voltage value can be converted into a binary number. This series of binary numbers can then be saved as a sound file and can be recreated at anytime by turning the numbers back into their original voltages which can make speakers or headphones vibrate so they recreate the sound.




