Lesson 2, Topic 4
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# Binary Arithmetic Operations – Multiplication

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Multiplication in binary is exactly as it is in decimal.

The four major steps in binary digit multiplication are:

0 x 0 = 0
0 x 1 = 0
1 x 0 = 0
1 x 1 = 1 (No borrow or carry method is applicable here)

a. Find the product of 1101two and 111two

1st Column (from right to left) = 1 + 0 = 1. 1 is less than 2, We write down 1.

2nd Column = 0 + 1 = 1. We write down 1.

3rd Column = 1 + 0 + 1 = 2. How many twos are there in 2? $$\frac{2}{2}$$ = 1 remainder 0. Write 0 and carry 1 to column 4.

4th column = 1 + 1 + 1 + 0 = 3. How many twos are there in 3? $$\frac{3}{2}$$ = 1 remainder 1. Write 1 and carry 1 to column 5.

5th column = 1 + 1 + 1 = 3. How many twos are there in 3? $$\frac{3}{2}$$ = 1 remainder 1. Write 1 and carry 1 to column 6.

6th column = 1 + 1 = 2. How many twos are there in 2? $$\frac{2}{2}$$ = 1 remainder 0. Write 0 and carry 1 to column 7.

7th column = We write down 1.

b. Multiply 11.01two by 1.1two

Answer = 100.1112 (count 3 decimal places from right to left)

c. 111two x 110two

d. 111two  x 111two

1st Column (from right to left) = 1. We write down 1.

2nd Column = 1 + 1 = 2. How many twos are there in 2? $$\frac{2}{2}$$ = 1 remainder 0. Write 0 and carry 1 to column 3.

3rd Column = 1 + 1 + 1 + 1 = 4. How many twos are there in 4? $$\frac{4}{2}$$ = 2 remainder 0. Write 0 and carry 2 to column 4.

4th column = 2 + 1 + 1 = 4. How many twos are there in 4? $$\frac{4}{2}$$ = 2 remainder 0. Write 0 and carry 2 to column 5.

5th column = 2 + 1 = 3. How many twos are there in 3? $$\frac{3}{2}$$ = 1 remainder 1. Write 1 and carry 1 to column 6.

7th column = We write down 1.