# The binary system 1+1=

The third digit can equal 4 or 0. The fourth digit can equal 8 or 0. If you write down the decimal values of each of the digits and then add them up, you have the decimal value of the binary number. In the case of binary 11, there is a 1 in the first position, which equals 1 and then another 1 in the second position, so that equals 2.

As numbers get larger, new digits are added to the left. To determine the value of a digit, count the number of digits to the left of it, and multiply that number times 2. For example, for the digital number , to determine the value of the 1, count the number of digits to the left of the 1 and multiply that number times 2. The total value of binary is 4, since the numbers to the left of the 1 are both 0s. Now you know how to count digital numbers, but how do you add and subtract them?

Binary math is similar to decimal math. Adding binary numbers looks like that in the box to the right above. To add these binary numbers, do this: Start from the right side, just as in ordinary math. Write a 1 down in the solution area. According to our rule, that equals 0, so write 0 and carry the 1 to the next column. Any time you have a column that adds up to decimal 3, you write down a 1 in the solution area and carry a 1.

In the fifth column you have only the 1 that you carried over, so you write down 1 in the fifth column of the solution.

Computers rely on binary numbers and binary math because it greatly simplifies their tasks. Now you know how to count digital numbers, but how do you add and subtract them?

Binary math is similar to decimal math. Adding binary numbers looks like that in the box to the right above. To add these binary numbers, do this: Start from the right side, just as in ordinary math.

Write a 1 down in the solution area. According to our rule, that equals 0, so write 0 and carry the 1 to the next column. Any time you have a column that adds up to decimal 3, you write down a 1 in the solution area and carry a 1. In the fifth column you have only the 1 that you carried over, so you write down 1 in the fifth column of the solution.

Computers rely on binary numbers and binary math because it greatly simplifies their tasks. Since there are only two possibilities 0 and 1 for each digit rather than 10, it is easier to store or manipulate the numbers. Computers need a large number of transistors to accomplish all this, but it is still easier and less expensive to do things with binary numbers rather than decimal numbers. The original computers were used primarily as calculators, but later they were used to manipulate other forms of information, such as words and pictures.

In each case, engineers and programmers sat down and decided how they were going to represent a new type of information in binary form. The chart shows the most popular way to translate the alphabet into binary numbers only the first six letters are shown. Although it is pretty complicated to do so, sounds and pictures can also be converted into binary numbers, too.

The result is a huge array of binary numbers, and the volume of all this data is one reason why image files on a computer are so large, and why it is relatively slow to view video or download audio over an internet connection.

Binary Numbers and Binary Math.