1011B x 11b = 1011b + 10110B = 100001B
See if you can decode this binary multiplication!
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To do binary addition, write the numbers with their columns lined up like you would with regular numbers:
111B
+ 110B
Then add the columns, starting from the ones column and move up. The following three facts should help you:
0B + 0B = 0B
1B + 0B = 1B
1B + 1B = 10B
Don’t forget to carry when you add two 1s together!
111B
+ 110B
––––––
1101B
To check your answer, you can convert it to standard decimal numbers:
111B = seven, 110B = six, 1101B = thirteen, so:
Seven + six = thirteen
What’s happening?
If you do this activity, you might think that binary is complicated and slow. In the example above, it takes four steps to add six and seven. However, most arithmetic in the world is done in binary – because most arithmetic is done by computers.
Binary numbers are written with only two digits: 1 and 0. A computer can store a binary number using open or closed switches to represent each digit. It is also easier to design chips to add binary. There are only three addition facts needed to make a binary adder work (0 + 0 = 0, 1 + 0 = 1, 1 + 1 = 10). A decimal adding machine would need 55 facts.
The binary system was formally described by Gottfried Leibniz about 300 years ago. Gottfried based his binary system on ideas he found in a fortune telling system known as I Ching. Leibniz though that binary would make a good system for computation, but it was hundreds of years before the first binary computers were made.
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