Binary addition. Just as in decimal, it is possible to carry out addition of binary numbers. The way to do this is through the column method. However, we need to remember some important rules as we only use ones and zeros in binary addition. zero plus zero equals 01 plus zero equals one, zero plus one equals one. One plus one equals zero, carry one, and one plus one plus one equals one, carry one.
These are the rules that must be adhered to when carrying out binary addition. Here we have our first example of binary addition. We have two binary numbers to add together. The first 110 is the binary for two and the second 101 is the binary For one, looking at the right hand column, we can see that we need to add together a zero and a one under the rules for binary zero plus one equals one, and we therefore put that at the bottom in the right hand column. Now looking at the left hand column, we have a one and zero, which we need to add together and following the rules of binary one plus zero equals one, which we put in the bottom of the left hand column. This gives us the binary number one one, which is the answer three in decimal.
And if we do the question in decimal two plus one equals three. Here we have a second example. In this example, both are binary numbers and 01, which is the binary equivalent of one decimal. Looking at the right hand column, this time we have one and one to add together under the binary rule prediction, one plus one equals zero carry one. And we can see that's been completed on the calculation. Now looking at the left hand column, we've got zero plus zero plus the one that we can read, which gives us a total of one, giving us a final answer in binary of one zero, which is the decimal number two.
If we do the calculation decimal, one plus one equals two, so the answer is correct. A final example. This time our two binary numbers are both one one, which in decimal is the equivalent of three. In the right hand column we have one plus one which under the binary rules for addition gives us zero carry one. This has been carried out on the question. In the middle column, we have one plus one plus the one that we carried.
And this gives us one carry one under the binary rules tradition. And again, this has been carried data on the question. We finally therefore have the left column where we have the one that we carried, which we must put in. This gives us a final answer in binary of 110, which is the equivalent of six in decimal. And if we do the question in decimal, three plus three equals six. Now it's your turn to try one.
Pause the video whilst you have a go as the answer is on the following slide. In this example, we have the two binary numbers 101, which is five in decimal, and 01, which is one in decimal. In the right hand, column one plus one equals zero carry one. In the middle column zero plus zero plus the one we carry gives us one, and it's in the left column one plus nothing gives us one. This gives us final answer in binary of 110, which is six index And if we do the question in decimal, five plus one equals six another example for you to have a go at. Pause the video whilst you give it a go.
In this question are two binary numbers are 111, which is the decimal equivalent for seven and 101, which is the decimal equivalent for five. Looking at the question in the far right column, we have one plus one which gives us zero carry one. coming across, we have one plus zero plus the one we carried which gives us a zero carry one. We then have one plus one plus the one we carry, which gives us one carry one. And then in the leftmost column, we have one plus nothing, which gives us one. I find the answer therefore it in binary is 1100, which is the decimal equivalent of 12.
If we do The question decimal seven plus five gives us 12. It's final question for you to try on this topic. Pause the video watch, do you have a goal? In this question, we have three binary numbers to add together. However, the technique doesn't change. Our first binary number 111 is the decimal equivalent of seven.
Our second binary number 01 is the decimal equivalent of one. And our third binary number 100 is the decimal equivalent of for looking at the right hand column, we have one plus one plus zero, which gives us zero carry one which has been completed on the question. We then have one plus zero plus zero plus the one we carried which gives us zero carry one. This again has been completed on the question. We then have one plus one plus the one we carried which gives us One carry one, and again this has been completed. And then in the left hand column we have one plus nothing which gives us one.
Our final answer therefore is 1100, which is 12 in decimal. And if we carry out the question decimal, seven plus one plus four gives us the answer is therefore correct