The Binary Number System

Part 4 - Multiplication

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 = 1Following these rules, we multiply using the standard

algorithm.The nice thing is that there is no carry or borrowing.

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

Multiplication Example

• Step 3, multiply the first 11 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 1 0 1 0 0 1

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

Check your work with decimal

• Translate our first factor:0 0 1 0 1 0 0 1 = 4110

• Translate our second factor:1 1 0 = 610

• Translate our answer:1 1 1 1 0 1 1 0 = 24610

• 41 x 6 = 246• 246 = 246 !

Verify answer with decimal

• Translate binary to decimal: 1001002=3610

• Translate binary to decimal: 11112=1510

• Translate binary to decimal: 101012=2110

• Check 36-15 = 21• 21 = 21 !

Videos on Multiplying in Binary

The first video shows a quick example: http://www.youtube.com/watch?v=Oza8QW5V7Qc

This second video shows the basics and some shortcuts: http://www.youtube.com/watch?v=QW0XNZPyWUk

The third video is a little more comprehensive and a little longer: http://www.youtube.com/watch?v=PpSxQ-IL_5Y

Multiplication Problems

• Without translating into decimal, do the following binary math problems

• Check your math by translating into decimal1) 10 x 10 =2) 100 x 11 =3) 101 x 10 =4) 11011 x 101 = 5) 101101 x 1101 = 6) 1010101 x 1011 =

€

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.