Collegedunia Team Content Curator
Content Curator
Binary multiplication is an operation performed on binary digits. Binary is a system of denoting numerical notation that has a base 2 rather than the normal denotation which is of base 10. It comprises zeros and ones rather than the base 10 notation numbers which comprise of 0 to 9 digits. The binary operations, when performed, have a similar procedure as the conventional operations. The only difference is the digits included. Binary addition, subtraction, multiplication and division includes just 1s and 0s, the rest steps are the same.
| Table of Content |
Key terms: Binary operations, binary multiplication, zero, one, decimal numbers, binary notations, digits, multiplication
Rules for Binary Multiplication
[Click Here for Sample Questions]
Multiplication of binary numbers abide by the following four binary multiplication rules:
- 0 × 0 = 0
- 1 × 0 = 0
- 0 × 0 = 0
- 1 × 1 = 1
Steps To Multiply Two Binary Numbers
[Click Here for Sample Questions]
Step one: Write both the multiplicand and multiplier one below the other.
Step two: Multiply the digit on the rightmost side of the multiplier (the number written below) with all the digits of multiplicand (the number written above). This rightmost digit is known as Least Significant Bit or LSB.
Step three: Now, leave a blank space below the rightmost digit while multiplying the digit of the next order of multiplier.
Step four: Keep repeating the process until the leftmost digit of the multiplier and the multiplicand is reached. This leftmost digit is known as Most Significant Bit or MSB.
Step five: The result at the end of this process will be the partial answer. The final answer will be obtained after adding the digits in the same sequence as they are placed, just like in conventional mathematical notation.
Binary Multiplication: Uses And Application
[Click Here for Sample Questions]
Binary multiplication is used in digital electronics. It is applied mostly to calculate the truth table of AND gate.
Binary Multiplication Table
[Click Here for Sample Questions]
Binary multiplication table is shown below:
| Binary Number | Multiplication Value |
|---|---|
| 0 x 0 | 0 |
| 1 x 0 | 0 |
| 0 x 1 | 0 |
| 1 x 1 | 1 |
Things to Remember
[Click Here for Sample Questions]
- Binary multiplication is done on binary digits.
- Binary digits include 0s and 1s.
- Procedure of operations remain same as conventional methods.
- Write multiplicand and multiplier one below the other.
- Multiply LSB with all digits of multiplicand.
- Repeat the process until MSB is reached.
- Add all the partial answers to get the complete answer.
Sample Questions
Ques. 10111 by 1101 (3 marks)
Ans.
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.
Hence the required product is 100101011.
Ques. Is it true that all binary operations are completed? (2 marks)
Ans. Certain binary operators may shut down some sets you might be familiar with, but many others will not. As a consequence, the number of odd integral parts has been closed. The number of strange integers, for example, isn't closed because the sum of two strange numbers isn't always strange, and it's never strange.
Ques. 11011.101 by 101.111 (3 marks)
Ans.
1 1 0 1 1 . 1 0 1
1 0 1 . 1 1 1
1 1 0 1 1 . 1 0 1
1 1 0 1 1 1 . 0 1 ← First partial product
1 0 1 0 0 1 0 1 1 1 ← First intermediate sum
1 1 0 1 1 1 0 1
1 1 0 0 0 0 0 1 0 1 1 ← Second intermediate sum
1 1 0 1 1 1 0 1
1 1 0 0 1 1 1 1 0 0 1 1 ← Third intermediate sum
1 1 0 1 1 1 0 1
1 0 1 0 0 0 1 0 0 1 0 0 1 1
Hence the required result is 10100010.010011.
Ques 3. Compute (10)2 * (11)2 (3 marks)
Ans. We can get an output by converting the binary numbers to respective numbers with base 10 and multiplying them to get the final output.
Here, (10)2 = (2)10, (11)2 = (3)10 and (110)2 = (6)10.
When we multiply 2 and 3, we will get the product as 6, which we are getting by multiplication of binary numbers. Hence our solution is correct.
Ques. Is square root a binary operation? (2 marks)
Ans. A non-binary transaction is a process that only requires one number to complete a task. Addition, subtraction, multiplication, and division are examples of binary operations. Square roots, factorials, and absolute values are typical non-binary operations.
Ques. Compute (111)2 * (101)2 (2 marks)
Ans. Therefore, the result is (111)2 * (101)2 = (100011)2
Ques. Compute (1010.01)2 * (1.01)2 (2 marks)
Ans. Therefore, the result is (1010.01)2 * (1.01)2 = (1100.1101)2
Ques. Multiply 11101 * 1001 (3 marks)
Ans. Therefore, the product of (11101)2 and (1001)2 is (100000101)2.
Verification
The decimal equivalent of (100000101)2 comes out to be 261. The decimal equivalent of (11101)2 comes out to be 29 and the decimal equivalent of (1001)2 comes out to be 9. Upon multiplication of 29 and 9, the product is 261. The decimal equivalent of (100000101)2 comes out to be 261. Hence, the product is correct.
Ques. What is the identity element of a binary operation? (2 marks)
Ans. A binary element, also known as a neutral element, is a type of element in a set that does not affect an element of the set when it is combined with the binary function. This description is used in algebraic structures like groups and rings.
Ques. What is a binary overflow? (2 marks)
Ans. Overflow occurs when the size of the bit field exceeds the size of a number. Overflow is possible in this situation because the bit fields of the two numbers that have been labeled with the same signature are very different.
Ques. Multiply 1101 * 1110 (3 marks)
Ans.
| Decimal | Binary |
|---|---|
| 13 x14 182 | 1101 x1110 0000 1101 1101 +1101 10110110 |
Ques. 1010 * 0110 (3 marks)
Ans.
| Decimal | Binary |
|---|---|
| 10 x6 60 | 1010 x0110 0000 1010 1010 +0000 0111100 |
Also read:
Comments