Binary multiplication

One of the mathematical operations done on binary integers or binary digits is binary multiplication. It’s comparable to the way decimal values are multiplied in arithmetic multiplication. In binary multiplication, however, only the digits 0 and 1 are employed because these are the only components of the binary number system. The binary multiplication operation is carried out step by step utilizing only 0s and 1s. A binary product is the result of the multiplication of binary numbers. Only the digits 0 and 1 make up the binary product. 

The product’s binary point is then placed in front of the total number of places counted from right. It’s worth noting that multiplying by zero makes the partial product’s bits all zero, so it may be ignored in intermediate steps. Multiplication by one also keeps the bits of the multiplicand the same but shifts them one bit to the left. By performing interim sums of partial products, binary number multiplication becomes more convenient.

Rule of Binary multiplication

Multiplication of binary numbers is analogous to the multiplication of decimal numbers. A multiplier and a multiplicand are both present. Multiplication yields a result, which is a product. Because binary multiplication uses just binary digits, we can only multiply 0s and 1s. The following are the rules for binary multiplication.

Multiplying binary integers is analogous to multiplying base-10 values (0 to 9). Only 0s and 1s make up binary numbers. As a result, we must know the product of 0 multiplied by 0 and 1 and 1 multiplied by 0 and 1. The following are the rules for binary multiplication.

• 0 × 0 = 0
• 0 × 1 = 0
• 1 × 0 = 0
• 1 × 1 = 1

Binary multiplication solved examples

A few examples will help you understand how binary multiplication works:

Example:1 multiply 10111 by 1101

                                1 0 1 1 1

                                   1 1 0 1

                                 1 0 1 1 1           ← First partial product

                            1 0 1 1 1     

                            1 1 1 0 0 1 1           ← First intermediate sum

                         1 0 1 1 1          

                       1 0 0 1 0 1 0 1 1           ← Final sum.

As a result, the needed product is 100101011.

Procedure and Binary long multiplication example

Multiplying binary numbers is similar to and easier than multiplying decimal numbers since binary numbers only have two digits: 0 and 1. The following is a method for multiplying binary numbers. The same restrictions apply to binary numerals that include a decimal point.

Step 1: Write the specified binary values one below the other, as in the traditional way of multiplication. The multiplicand is the number above the multiplier, while the multiplier is the number below the multiplicand. For example, the binary numbers (1101)₂ and (1010)₂ can be multiplied.

(1101)₂

X (1010)₂

Step 2: To begin multiplication, we look at the digit in the right-hand corner. Taking the digit from the extreme right, multiply it by the multiplicand’s extreme right digit and continue in the same manner to the multiplicand’s left.

1101

X 1010

___________

= 0000

Step 3: Using the same method for the rest of the multiplicand and multiplier digits, we get

1101

X1010

                                                                     ___________

= 0000

1101X

0000XX

1101XXX

___________

Step 4: To get the final product, add all of the figures you’ve gotten so far. When all of the intermediate products are added together, we get

1101

X1010

___________

= 0000

1101X

0000XX

+1101XXX

___________

Step 5: Before adding all the numbers, remember to use the binary digit addition rule.

0 + 0 = 0

0 + 1 = 1

1 + 0 = 1

1 + 1 = 10

When you add 1 to itself in binary, the result is 10 and is written with a 0 in the spot and a 1 carried to the next number. Then we add binary numbers together to get,

1101

X1010

___________

= 0000

1101X

0000XX

+1101XXX

___________

10000010

___________

As a result, (10000010)2 is the binary multiplication of (1101)2 and (1010)2.

Conclusion

We learn that the process of multiplying binary numbers is known as binary multiplication. The process of multiplying binary numbers is the same as multiplying decimal values arithmetically. In digital systems, a binary multiplier is a combinational logic circuit that performs the multiplication of two binary values. These are widely utilized in a variety of applications, particularly in the field of digital signal processing, to carry out various algorithms.