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.
In this article, we will learn about Binary Numbers, Binary multiplication, and Rules to perform Binary multiplication, accompanied by solved examples, practice problems, and answers to frequently asked questions.
What is Binary Multiplication?
Binary multiplication is a mathematical operation performed on binary numbers, which are composed of only the digits 0 and 1. We use 0 to 9 in the case of decimal division, whereas 0’s (zeros) and 1’s (ones) are used in binary multiplication.
- Similar to decimal multiplication, 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.
Learn, Multiplication
Before learning more about Binary Multiplication, let’s first learn about Binary Numbers
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 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 division of Binary Multiplication. Binary Multiplication rules is shown in the Binary Multiplication Table below:
Binary Multiplication Table
The rules for Binary Multiplication is tabulated below:
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0 × 0 = 0
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If 0 (zero) is multiplied to another 0 (zero), then the result is 0 (zero).
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0 × 1 = 0
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If 0 (zero) is multiplied to 1 (one), then the result is 0 (zero).
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1 × 0 = 0
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If 1 (one) is multiplied to 0 (zero), then the result is 0 (zero).
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1 × 1 = 1
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If 1 (one) is multiplied to another 1 (one), then the result is 1 (one).
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How to do Binary Multiplication?
There are five key steps involved in Binary Multiplication that are,
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 Binary Multiplication Calculator to easily calculate multiplication of two binary numbers.
Binary Multiplication Calculator
The binary multiplication calculator added below easily multiply two binary numbers.
Examples of Binary Multiplication
Some examples on Binary Multiplication are,
Example 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.
(1010)2 x (101)2
So, the product of (1010)2 ÷ (101)2 is (110010)2
Example 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.
(1101)2 x (100)2
So, the product of (1101)2 ÷ (100)2 is (110100)2
Example 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.
(0.101)2 x (0.11)2
So, the product of (0.101)2 ÷ (0.11)2 is (0.01111)2
Example 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.
(101.01)2 x (110)2
So, product of (101.01)2 ÷ (110)2 is (11111.10)2
Example 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.
(1111)2 × (1010)2
So, the product of (1111)2 ÷ (1010)2 is (10010110)2
Also, Check Binary Formula
Binary Multiplication Practice Questions
Some Question on Binary Multiplications are,
Q1. Multiply (1110)2 by (10)2
Q2. Multiply(10010101)2 by (11)2
Q3. Multiply (1001)2 by (1001)2
Q4. Multiply (1110010)2 by (111)2
Q5. Multiply (110.10)2 by (101)2
Binary Multiplication – Frequently Asked Questions
What is Binary Multiplication?
Process of multiplying binary numbers is called binary multiplication.
Is Binary Multiplication same as Decimal Multiplication?
Yes, We use 0 (zero) to 9 in case of decimal multiplication, whereas 0’s (zero) and 1’s (ones) are used in binary multiplication.
Is Binary Multiplication Commutative?
Yes, Binary Multiplication is commutative, the order of the numbers does not affect the result. A × B = B × A
What are Rules of Binary Multiplication?
Rules of Binary Multiplication are
- 0 x 0 = 0
- 0 x 1 = 0
- 1 x 0 = 0
- 1 x 1 = 1
What is Binary Product of 1001 and 1011?
Binary product of 1001 and 1011 is 1100011.
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