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The Binary Number System

The Binary Number System. Part 5 - Division. General Information. To divide, we use the same algorithm as we do with decimal numbers. The nice thing is that with decimal numbers, you only have 0 – the number doesn’t fit and 1 – the number does fit.

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The Binary Number System

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  1. The Binary Number System Part 5 - Division

  2. General Information To divide, we use the same algorithm as we do with decimal numbers. The nice thing is that with decimal numbers, you only have 0 – the number doesn’t fit and 1 – the number does fit. As with decimal division, binary division is a series of multiplying and subtracting in binary, so you need to know those fairly well before you attempt division.

  3. Division Example • Let’s say we want to do • Step 1: Set up the problem • Step 2: Can we get a 11 out of 1? No, put a 0. • Step 3: Can we get a 11 out of 10? No, put a 0.

  4. Division Example • Step 4: Can we get 11 out of 100? Yes, so it is a 1. So then we multiply 11 x 1 = 11 and we subtract that from 100 (100 – 11) and we get 1. • Step 5: bring down the next 1, to make 11 and we can get one 11 out of 11.

  5. Checking our Division Example • To check our work we can do 2 ways: • Verify with decimals • Multiply the quotient with the divisor and make sure we get the dividend • Verifying with decimals: • 10012 = 910 (dividend) • 112 = 310 (divisor & quotient) • 9/3 = 3 and 3=3, so it worked!

  6. Check your work with multiplication Multiply 11 x 11 and see what you get: 1 1 X1 1 1 1 1 1 0 1 0 0 1 Given that we got the dividend we started with, our division checks out this way as well.

  7. Websites on Dividing in Binary The first website explains in words with examples: http://www.exploringbinary.com/binary-division/ This video gives a few examples: http://www.youtube.com/watch?v=dlKl9k_UdX0 This video is longer and gives more examples of dividing: http://www.youtube.com/watch?v=SqIpxX14nUs This explanation allows you to step through an example: http://courses.cs.vt.edu/~csonline/NumberSystems/Lessons/Division/index.html

  8. Division Problems • Without translating into decimal, do the following binary math problems • Check your math by translating into decimal • Check your math with binary multiplication • 1111/101 = • 101010/111 = • 110110110/110 = • 111100/100 = • 1111100/1000 = • 110100100/1000 =

  9. Work to do to complete this unit • Problems on page 8 of this packet • Name 3 things important to dividing in binary: • ______________________________ • ______________________________ • ______________________________ • Create 5 of your own new binary division problems, do them, check your work and turn in. At least 3 of the problems must havedividends with more than 5 digits.

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