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 1101_{two} and 111_{two}

**Explanation on addition**

**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.

**Answer** = 1011011_{2}

**b.** Multiply 11.01_{two} by 1.1_{two}

**Answer** = 100.111_{2} (count 3 decimal places from right to left)

**c. **111_{two} x 110_{two}

**d.** 111_{two} x 111_{two}

**Explanation on addition**

**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.

**Answer** = 110001_{2}

**e. **11101 x 110

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