1. The Binary Number System Part 4 - Multiplication

2. General Rules The rules for binary multiplication are the same as they are for decimal: 0 x 0 = 0 1 x 0 = 0 0 x 1 = 0 1 x 1 = 1 Following these rules, we multiply using the standard algorithm. The nice thing is that there is no carry or borrowing.

3. Multiplication Example Let’s say we want to do 101001 × 110 Step 1: Set up the problem: 1 0 1 0 0 1 × 1 1 0 Step 2: The first row will be all 0’s because 0 times anything is still 0: 1 0 1 0 0 1 × 1 1 0 0 0 0 0 0 0

4. Multiplication Example Step 3, multiply the first 1 1 0 1 0 0 1 × 1 1 0 0 0 0 0 0 0 1 0 1 0 0 1 Step 4, multiply the second 1 1 0 1 0 0 1 × 1 1 0 0 0 0 0 0 0 1 0 1 0 0 1

5. Multiplication Example Step 5: Add them up 1 0 1 0 0 1 × 1 1 0 0 0 0 0 0 0 1 0 1 0 0 1 + 1 0 1 0 0 1 1 1 1 1 0 1 1 0

6. Check your work with decimal Translate our first factor: 0 0 1 0 1 0 0 1 = 41 10 Translate our second factor: 1 1 0 = 6 10 Translate our answer: 1 1 1 1 0 1 1 0 = 246 10 41 x 6 = 246 246 = 246 !

7. Verify answer with decimal Translate binary to decimal: 100100 2 =36 10 Translate binary to decimal: 1111 2 =15 10 Translate binary to decimal: 10101 2 =21 10 Check 36-15 = 21 21 = 21 !

8. Videos on Multiplying in Binary The first video shows a quick example: http://www.youtube.com/watch?v=Oza8QW5V7 Qc http://www.youtube.com/watch?v=Oza8QW5V7 Qc This second video shows the basics and some shortcuts: http://www.youtube.com/watch?v=QW0XNZPy WUk http://www.youtube.com/watch?v=QW0XNZPy WUk The third video is a little more comprehensive and a little longer: http://www.youtube.com/watch?v=PpSxQ-IL_5Y http://www.youtube.com/watch?v=PpSxQ-IL_5Y

9. Multiplication Problems Without translating into decimal, do the following binary math problems Check your math by translating into decimal 1)10 x 10 = 2)100 x 11 = 3)101 x 10 = 4)11011 x 101 = 5)101101 x 1101 = 6)1010101 x 1011 =

10. Work to do to complete this unit Problems on page 9 of this packet Name 3 things important to multiplying in binary: 1.______________________________ 2.______________________________ 3.______________________________ Create 5 of your own new binary multiplication problems, do them, check your work and turn in. At least 3 of the problems must have more than 5 digits.