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: – 1001 2 = 9 10 (dividend) – 11 2 = 3 10 (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/ http://www.exploringbinary.com/binary-division/ This video gives a few examples: http://www.youtube.com/watch?v=dlKl9k_UdX0 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 http://www.youtube.com/watch?v=SqIpxX14nUs This explanation allows you to step through an example: http://courses.cs.vt.edu/~csonline/NumberSyste ms/Lessons/Division/index.html http://courses.cs.vt.edu/~csonline/NumberSyste ms/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 1)1111/101 = 2)101010/111 = 3)110110110/110 = 4)111100/100 = 5)1111100/1000 = 6)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: 1.______________________________ 2.______________________________ 3.______________________________ Create 5 of your own new binary division problems, do them, check your work and turn in. At least 3 of the problems must have dividends with more than 5 digits.