Binary Multiplication is a mathematical operation that involves multiplying two binary numbers, which are numbers composed of only 0s and 1s. Binary multiplication is similar to decimal multiplication, except that the base of the number system is 2 instead of 10.
- Binary multiplication involves multiplying each bit of the first number by each bit of the second number, and then adding the results.
- Binary multiplication is fundamental in computer science and digital systems, as binary is the foundational numeral system for representing information in computers.
Binary Multiplication
In this article, we will learn about Binary Numbers, Binary multiplication, and the rules to perform Binary multiplication, accompanied by solved examples.
What are Binary Numbers?
Binary Number is a number that is used to represent various numbers using only two symbols, “0” and “1”.
- Binary numbers are expressed in the base-2 numeral system.
- Each digit in this system is called a bit.
Example of a Binary Number: Binary of Equivalent of 6 = (110)2
Learn More, Binary Number System
Binary Multiplication Rules
Binary Multiplication is performed in the same manner as decimal numbers are multiplied. However, there are some specific rules regarding the multiplication among the binary digits 0 and 1, which we need to follow while performing the division of Binary Multiplication. Binary Multiplication rules are shown in the Binary Multiplication Table below:
Binary Multiplication Table
The rules for Binary Multiplication are tabulated below:
Table for Binary Multiplication Rule |
|---|
Rules for Multiplication | Meaning |
|---|
0 × 0 = 0 | If 0 (zero) is multiplied by another 0 (zero), then the result is 0 (zero). |
0 × 1 = 0 | If 0 (zero) is multiplied by 1 (one), then the result is 0 (zero). |
1 × 0 = 0 | If 1 (one) is multiplied by 0 (zero), then the result is 0 (zero). |
1 × 1 = 1 | If 1 (one) is multiplied by another 1 (one), then the result is 1 (one). |
Binary Multiplication Calculator
The binary multiplication calculator added below can easily multiply two binary numbers.
How to do Binary Multiplication?
There are five key steps involved in Binary Multiplication:,
Step 1: Write the multiplicand and the multiplier one below the other, aligning the rightmost digits.
Step 2: Multiply the multiplicand by each digit of the multiplier, starting from the rightmost digit.
Step 3: Move to the next digit of the multiplier and multiply it by the multiplicand. Write the result below the multiplier after shifting it to the left by one position.
Step 4: Repeat this process for each digit of the multiplier, shifting the result to the left by one more position each time.
Step 5: Add all the results using binary addition rules. The final sum is the product of the two binary numbers.
You can also use the Binary Multiplication Calculator to easily calculate the multiplication of two binary numbers.
Solved Question on Binary Multiplication
Question 1: (1010)2 × (101)2
Solution:
Step 1: Write the multiplicand (1010)2 and the multiplier (101)2 one below the other, aligning the rightmost digits.
Step 2: Multiply the multiplicand by each digit of the multiplier, starting from the rightmost digit. The rightmost digit of the multiplier is 1, so we write down the multiplicand as it is.
Step 3: Move to the next digit of the multiplier and multiply it by the multiplicand. The next digit of the multiplier is 0, so we write down 0 after shifting it to the left by one position.
Step 4: Move to the next digit of the multiplier and multiply it by the multiplicand. The next digit of the multiplier is 1, so we write down the multiplicand after shifting it to the left by two positions.
Step 5: Add all the results using binary addition rules. The final sum (110010)2 is the product of the two binary numbers.
So, the product of (1010)2 × (101)2 is (110010)2
Question 2: (1101)2 × (100)2
Solution:
Step 1: Write the multiplicand (1101)2 and the multiplier (100)2 one below the other, aligning the rightmost digits.
Step 2: Multiply the multiplicand by each digit of the multiplier, starting from the rightmost digit. The rightmost digit of the multiplier is 0, so we write down 0.
Step 3: Move to the next digit of the multiplier and multiply it by the multiplicand. The next digit of the multiplier is 0, so we write down 0 after shifting it to the left by one position.
Step 4: Move to the next digit of the multiplier and multiply it by the multiplicand. The next digit of the multiplier is 1, so we write down the multiplicand after shifting it to the left by two positions.
Step 5: Add all the results using binary addition rules. The final sum (110100)2 is the product of the two binary numbers.
So, the product of (1101)2 × (100)2 is (110100)2
Question 3: (0.101)2 × (0.11)2
Solution:
Step 1: Write the multiplicand (0.101)2 and the multiplier (0.11)2 one below the other, aligning the rightmost digits.
Step 2: Multiply the multiplicand by each digit of the multiplier, starting from the rightmost digit. The rightmost digit of the multiplier is 1, so we write down the multiplicand as it is.
Step 3: Move to the next digit of the multiplier and multiply it by the multiplicand. The next digit of the multiplier is 1, so we write down the multiplicand after shifting it to the left by one position.
Step 4: Move to the next digit of the multiplier and multiply it by the multiplicand. The next digit of the multiplier is 0, so we write down 0 after shifting it to the left by two positions.
Step 5: Add all the results using binary addition rules. The final sum (001111)2 is the product of the two binary numbers.
Step 6: Count the total number of digits (d) after the decimal point in both the multiplicands and the multiplier. Place the decimal point in the product after (d) digits from right side.
So, the product of (0.101)2 × (0.11)2 is (0.01111)2
Question 4: (101.01)2 × (110)2
Solution:
Step 1: Write the multiplicand (101.01)2 and the multiplier (110)2 one below the other, aligning the rightmost digits.
Step 2: Multiply the multiplicand by each digit of the multiplier, starting from the rightmost digit. The rightmost digit of the multiplier is 0, so we write down 0.
Step 3: Move to the next digit of the multiplier and multiply it by the multiplicand. The next digit of the multiplier is 1, so we write down the multiplicand after shifting it to the left by one position.
Step 4: Move to the next digit of the multiplier and multiply it by the multiplicand. The next digit of the multiplier is 1, so we write down the multiplicand after shifting it to the left by two positions.
Step 5: Add all the results using binary addition rules. The final sum (1111110)2 is the product of the two binary numbers.
Step 6: Count the total number of digits (d) after the decimal point in both the multiplicands and the multiplier. Place the decimal point in the product after (d) digits from right side.
So, product of (101.01)2 × (110)2 is (11111.10)2
Question 5: (1111)2 × (1010)2
Solution:
Step 1: Write the multiplicand (1111)2 and the multiplier (1010)2 one below the other, aligning the rightmost digits.
Step 2: Multiply the multiplicand by each digit of the multiplier, starting from the rightmost digit. The rightmost digit of the multiplier is 0, so we write down 0.
Step 3: Move to the next digit of the multiplier and multiply it by the multiplicand. The next digit of the multiplier is 1, so we write down the multiplicand after shifting it to the left by one position.
Step 4: Move to the next digit of the multiplier and multiply it by the multiplicand. The next digit of the multiplier is 0, so we write down 0 after shifting it to the left by two positions.
Step 5: Move to the next digit of the multiplier and multiply it by the multiplicand. The next digit of the multiplier is 1, so we write down the multiplicand after shifting it to the left by three positions.
Step 6: Add all the results using binary addition rules. The final sum (10010110)2 is the product of the two binary numbers.
So, the product of (1111)2 × (1010)2 is (10010110)2
Also, check the Binary Formula
Binary Multiplication Practice Questions
Some questions on Binary Multiplications are,
Question 1: Multiply (1110)2 by (10)2
Question 2: Multiply(10010101)2 by (11)2
Question 3: Multiply (1001)2 by (1001)2
Question 4: Multiply (1110010)2 by (111)2
Question 5: Multiply (110.10)2 by (101)2