Introduction

The four basic arithmetic operations are addition, subtraction, multiplication, and division. We can use the mentioned four operations to obtain numerous different operations. In digital computers that handle data, arithmetic instructions are being used to rectify complex mathematical problems. 

Multiplication of Binary Numbers

The process of multiplying binary numbers is understood as binary multiplication. Multiplying binary numbers is just the same as multiplying decimal figures basic math multiplication. The one and the only difference is that binary multiplication comprises digits made up of 0s and 1s, whereas decimal multiplication comprises digits made up of digit numbers scale from 0 to 9. 

Rules for Binary Multiplication

Binary multiplication is equivalent to decimal system multiplication. There is a multiplier as well as a multiplicand factor involved. The result of the multiplication is really a product. Since binary multiplication is using only binary numbers, we can really only multiply 0s and 1s. The binary multiplication rules are as follows-

Multiplicand Value	Multiplier Value	Product (End Result)
0	0	0 × 0 = 0
0	1	0 × 1 = 0
1	0	1 × 0 = 0
1	1	1 × 1 = 1

Let us take the example of multiplying (11101)2 and (101)2. The decimal equivalent of (11101)2 is 29 and the decimal equivalent of (101)2 is 5. Now let us multiply these numbers.

Step 1: Write the multiplicand value (11101)2  and the multiplier value (101)2  one below the other in correct & appropriate positions.

Step 2: Multiply the digit which is towards the rightmost side or the least significant bit (LSB) of the multiplier value (1) with all the digits of the multiplicand value (11101)2.

Step 3: Add a ‘0’ or ‘X’ place holder prior to actually multiplying the next higher level order digit with the multiplicand.

Step 4: Repeat the process for the next higher-order digit numbers till we attain the most significant bit (MSB). This is referred to as the multiplicand’s leftmost digit with the multiplier.

Step 5: The partial product is the product derived within every row. Finally, combine all of the partial products. Use the binary addition rules to add all the binary numbers.

Let’s take a look at the above-mentioned binary multiplication process.

In the decimal system → 1

111012 = 2910

In the decimal system→ 2

1012 = 510

Their product

29 ✕  5 = 145

End Result in binary form

14510 = 100100012

Let’s Learn With A Few Examples Now:

Multiply 11101 & 10

Answer:

In the decimal system → 1

111012 = 2910

In the decimal system→ 2

102 = 210

Their Product

29 ✕ 2 = 58

Result in binary form

5810 = 1110102

Multiply 11011 & 1101

Answer:

In the decimal system → 1

110112 = 2710

In the decimal system→ 2

11012 = 1310

Their Product

27 ✕ 13 = 351

Result in binary form

35110 = 1010111112

Multiply 100111 & 101

Answer:

In the decimal system → 1

1001112 = 3910

In the decimal system→ 2

1012 = 510

Their Product

39 ✕ 5 = 195

Result in binary form

19510 = 110000112

Multiply 10001 & 110011

Answer:

In the decimal system → 1

100012 = 1710

In the decimal system→ 2

1100112 = 5110

Their Product

17 ✕ 51 = 68

Result in binary form

6810 = 10001002

Multiply 110111 & 101100

Answer:

In the decimal system → 1

1101112 = 5510

In the decimal system→ 2

1011002 = 4410

Their Product

55 ✕ 44 = 2420

Result in binary form

242010 = 1001011101002

Conclusion 

We discussed Basic Computer Operation & Arithmetic Operations related Division, the rules associated with the calculations, and other related topics through the study material notes on Basic Computer Operation-Arithmetic Operations-Division.

Trying to combine operands with one arithmetic provider specifies an arithmetic operation. The built-in functions ADD, SUBTRACT, DIVIDE, and MULTIPLY could also be used to clarify arithmetic operations. The plus and minus indications could be used as either prefix or infix operators.