How to Add Binary Numbers

If you have ever wanted to better understand how your computer works or just impress that really cute math whiz in your class, learning how to perform functions in binary is the perfect solution. Even if it seems foreign at first, you will soon discover that with just a little practice, you can be a brainiac yourself. Follow these steps to add binary numbers.

Instructions

1. Learn the language. Binary (or base two) only uses two numerals: 0 and 1. To represent numbers larger than one, binary uses place values, just as the base 10 system does. For example, in base 10, the number eleven is represented by 11, because a 1 is in the ones place and a 1 is in the tens place. One one plus one ten equals eleven. In binary, instead of each place representing a ten-times value increase, it represents a two-times value increase. So, 11 in binary equals three, because one one plus one two equals three. That means 111 in binary equals seven (four plus two plus one), and 1111 in binary equals fifteen (eight plus four plus two plus one) and so on.

2. Review addition in base 10. Adding in binary is just like adding in base 10. In base 10, if you add 19 + 22, you would first add the numbers in the "ones" place. Because the largest numeral you have to work with is 9, to represent any number larger than nine, you have to use two columns. We call this procedure carrying. Nine plus two equals eleven, and since eleven is greater than nine, we have to carry into the tens column. In the example 1 + 19 + 22, when you add the numbers in the tens column, one plus two, you can write the answer down in that same column without carrying because the answer, four, is also less than ten.

3. Understand binary addition. The same principles we reviewed in base 10 apply to adding in base 2, the binary system. Because the largest numeral you have to work with is 1, you have to represent any value larger than one by using more than one column. Once again, this is where the concept of carrying comes in.

4. Set up a base 2 problem. Let's try adding five and seven in binary: 101 + 111. First we add the ones column. One plus one equals two, and since we can't use any numeral larger than 1, we have to represent two by using the place values of the columns. A value of two doesn't fit in the first column because it is larger than one. So, we write a 0 down in the first column and carry our one over to the next column.

   1
   101
   +111
   _____
   0

5. Add the second column. Now we have one plus zero plus one. The answer, again, is a value of two. But, since we can't write a numeral larger than 1, we put a zero in the second column and carry our one to the third column.

6. Solve the third column. The third column now contains three ones, yielding a value of three. We know we can't write a numeral 3, so we have to represent the value three using place values. In binary, 11 represents the value of three because a 1 is in the place that represents the value of one and a 1 is in the place that represents a value of two. Therefore, one plus two equals three.

7. Check your answer by reading the value of the binary number. 101 + 111 = 1100 with the 1 furthest to the left in the place representing the value of eight. The next 1 is in the place representing the value of four. The other two places have no value since they have the numeral 0 in them. So, if we add the values together (eight plus four) we get an answer of twelve. And since we know five plus seven equals twelve, we know our binary answer is correct.

8. Practice your binary skills. Try writing, counting and adding in binary regularly. Before you know it, you'll be performing advanced mathematical functions using just two little numerals: 0 and 1.

Tips & Warnings

• Just remember: 0+0=0, 1+0=1 and 1+1=10