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Example 1: Add: 102 + 1002
Solution: The first step is to "line up" the digits, like we do for decimal numbers. We want to make sure that all of the digits in the same place value are beneath one another.
102
+ 1002
We start the addition process from the right, just as if we were adding decimal numbers. We know that zero plus zero equals zero no matter what number system is being used. We can write down the zero in the units place; we have no numbers to "carry."
102
+ 1002
0
The next step is to add the one and the zero. The sum of one and zero is one in any number base. We write down the one in the twos place and have no numbers to carry.
102
+ 1002
10
The final step is to look at the two to the second power place. Since we have not carried any numbers and there is no value in the two to the second power place in the first addend, all we need to do is bring down the one to obtain the answer.
102
+ 1002
1102
This shows that the sum of 102 plus 1002 equals 1102 .
Example 2: Add: 1102 + 1012
Solution: The first step is to "line up" the digits, like we do for decimal numbers. We want to make sure that all of the digits in the same place value are beneath one another.
1102
+ 1012
We start the addition process from the right, just as if we were adding decimal numbers. We know that one plus zero equals one no matter what number system is being used. We can write down the one in the units place; we have no numbers to "carry."
1102
+ 1012
1
The next step is to add the one and the zero. We know that their sum is one. We write down the one in the twos place and have no numbers to carry.
1102
+ 1012
11
The final step is to look at the two to the second power place. Since we have not carried any numbers we must just add one and one. Looking at the Table 3.3.1, we see that in the binary system 1 + 1 = 10. So, we can write 10 to obtain the answer.
1102
+ 1012
10112
This shows that the sum of 1102 plus 1012 equals 10112 .
Example 3: Add: 10112 + 1012
Solution: The first step is to "line up" the digits, like we do for decimal numbers. We want to make sure that all of the digits in the same place value are beneath one another.
10112
+ 1012
We start the addition process from the right, just as if we were adding decimal numbers. We know that one plus one equals 10 from Table 3.3.1. Since there is room for only one digit in the sum line, we must begin to carry numbers. When we carry, we use the same process as the decimal system, that is, we write down the digit on the right, in the units place, and carry the digit on the left (in this case, in the twos place.) We can write down the zero in the units place and carry the one.
1 "carried one"
10112
+ 1012
0
The next step is to add the one and the zero. We know that their sum is one. Now we must add the sum that we have just obtained with the "carried" one. One plus one is 10. We write down the zero in the twos place and carry the one to the two to the second place.
1 "carried one"
10112
+ 1012
00
The next step is to add the zero and the one. We know that their sum is one. Now we must add the sum that we have just obtained with the "carried" one. One plus one is 10. We write down the zero in the twos place and carry the one to the two to the third place.
1 "carried one"
10112
+ 1012
000
The final step is to look at the two to the third power place. We must add one and one to get 10. We write down the 10 to obtain the answer.
1 "carried one"
10112
+ 1012
100002
This shows that the sum of 10112 plus 1012 equals 100002 .
Example 4: Add: 11112 + 1112
Solution: The first step is to "line up" the digits.
11112
+ 1112
We start the addition process from the right. One plus one is 10. We write down the zero and carry the one.
1 "carried one"
11112
+ 1112
0
The next step is to add the one and the one in the addends. We know that their sum is 10. At this point, you may wish to carry the one to the next place.
1 1 "carried ones"
11112
+ 1112
0
Now we must add the remaining zero with the carried one. Since 0 + 1 = 1, we write down the one in the twos place.
1 "carried one"
11112
+ 1112
10
The next step is to add the one and the one. We know that their sum is 10. Carry the one.
1 1 "carried ones"
11112
+ 1112
10
Now add the zero left with the carried one to obtain a value of 1 to write in the two to the second power place.
1 "carried one"
11112
+ 1112
110
The final step is to look at the two to the third power place. We must add one in the first addend with the carried one to get 10. We write down the 10 to obtain the answer.
1 "carried one"
11112
+ 1112
101102
This shows that the sum of 11112 plus 1112 equals 101102 .
3.3 ~ Practice Problems
Directions: Turn off your VCR. Add the following numbers that are in binary notation. Turn the VCR back on to check your answers in the Answer Key.
3.3 ~ Homework Problems
Directions: Turn off your VCR. Add the following numbers that are in binary notation. Check your answers in the Answer Key. If you have any questions, contact your instructor.
THIS CONCLUDES SESSION THREE
Last Updated January 2004
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Begin this session by watching the video tape. If you have purchased a textbook, follow along in your book. If you are using the Internet version, follow along on the webpage. If you have any difficulties, contact your instructor. After the explanation of place values, turn off the video player and try to work the practice problems. Once you have worked the problems, check your answers in the answer key or click on the Answer Key Links.
