Binary Number System
The binary number system is used by computers to send a series of electrical signals representing information in a special cipher of 0's and 1's. Before you try to tackle the math of the binary number system, Base 2, it's probably a good idea to review what you already know, Base 10.
The Base 10 number systems makes use of 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Numbers above 9, such as 10, are actually a combination of numbers in the sequence above. In the case of 10 it is a combination of 1 and 0. This forces a positioning of the digits (like 1 and 0) into a given location within a number.
In the example of number 10 has two digits, 1 and 0. The 1 is the second digit to the left of the assumed decimal place. Because it is in the second position to the left of the decimal it has the value of 10. The 1 indicates that there is only 1 number in the placement value worth 10. The 1 indicates that there are no numbers for the placement value of 1. Look at the table below and fill in the placement values up to 1,000,000.
Placement Values ? ? ? 1,000 100 10 1
Notice any patterns about how the placement value increases as it proceeds to the left of the decimal? It goes up by a factor of 10. In other words, multiply the placement value by 10 and you get the next placement value! Similarly, once you have used all the digits in the Base 10 system, with 9 being the highest numbered digit, you are forced to use 10. That actually means that the 1 is in the next highest placement order and you give the lower placement order a value of 0. This unique and incredible mathematical placement system also holds true for the binary number system.
Can you figure out how many digits are used in the binary system? Two, 0's and 1's. Additionally, the Base 2 (binary) system placement values increase by a factor of 2. Can you figure out how that is similar to Base 10? Look at the placement table below and see if you can figure it out:
Placement Value 256 128 64 32 16 8 4 2 1
Using the table above can you figure out what follows 256 on the placement table? Take 256 X 2 and you have your answer, 512. The Base 10 number 3 is represented by 0's and 1's in the Base 2 number system as 11:
Placement Value 256 128 64 32 16 8 4 2 1
Decimal Value 1 1
That's 1 at a value of 2, and 1 at a value of 1. Thus, 2 + 1 = 3. Here's another example, translating the Base 10 number 17, written as 1710, into binary numbers (0's and 1's):
Placement Value 256 128 64 32 16 8 4 2 1
Decimal Value 1 0 0 0 1