**Binary multiplication** is one of another type of arithmetic. There are four type of binary arithmetic operation. That is addition, subtraction, multiplication and division. The binary multiplication is the type of binary arithmetic operation. In binary operation we only deals with two bit and that bit are “0” and “1”. The binary multiplication operation is similar the conventional multiplication. The difference in between binary multiplication and conventional multiplication is that, the conventional method uses ten numbers from 0 to 9 but binary uses only two numbers that are “0” and “1”. The binary digit multiplication has four rules:

- 0 × 0 = 0
- 0 × 1 = 0
- 1 × 0 = 0
- 1 × 1 = 1

Note: the binary bit product of 1 and 1 is 1. In this production there is no carry and no borrow. The multiplication of any number with zero is always zero. In this session we learn about process of binary multiplication step by step. In this article, we will get answers for the questions related with binary multiplication:

- What is Binary multiplication?
- Procedure to multiply two binary numbers
- Steps involves in Binary multiplication with examples

## What is Binary Multiplication?

In binary multiplication process we use addition and shifting operation. This process will be continuing when all bits multiply and finally do addition operation. It is similarly to the decimal system. When you multiply with zero make all bits to zero and this step may be ignored in the intermediate steps. The multiplication by 1 the result of multiplicand value same.

### Binary Multiplication Table

The binary bits multiplication table is given below.

Binary Number |
Multiplication Value |

0 x 0 | 0 |

1 x 0 | 0 |

0 x 1 | 0 |

1 x 1 | 1 |

## Binary Multiplication Rules

Binary multiplications is same as the rest binary operation; it is much easier than the decimal multiplication. You remember the rules of binary multiplications.

** The rules of binary multiplication are**:

- 0 × 0 = 0
- 0 × 1 = 0
- 1 × 0 = 0
- 1 × 1 = 1 [No borrow or carry method is required]

You are clearly seen the binary multiplication includes 0, and then it will result in zero itself. Hence,

Binary bits product of 0 and 0 is equal to 0

Binary bits product of 0 and 1 is equal to 0

Binary bits product of 1 and 0 is equal to 0

But,

Binary bits product of 1 and 1 is equal to 1.

Addition |
Subtraction |
Division |

0 + 0 = 0 | 0 – 0 = 0 | 0 ÷ 0 = 0 |

0 + 1 = 1 | 0-1 = 1 [the borrow is 1] | 0 ÷ 1 = 0 |

1 + 0 = 1 | 1 – 0 = 1 | 1 ÷ 1 = 1 |

1+1 = 0 (1 is carry forwarded is 1) | 1 – 1 = 0 |

### How to do binary multiplication

Binary bit multiplications is similar and easier to decimal multiplications. Binary bit contain only two bit that are “0” and “1”. The binary bit multiplications rule is described below. Let us see the one example of multiplication (11101)_{2}_{ }and (1001)_{2}_{.}. The decimal equivalent of (11101)_{2}_{ }is 29 and the decimal equivalent of (1001)_{2}_{ }is 9. Let us see the step by step.

**Step 1:** Write multiplicand (11101)_{2}_{ }and the multiplier (1001)_{2}_{ }one below the other in proper positions.

**Step 2:** Multiply the rightmost digit or least significant bit (LSB) of the multiplier (1) with all the digits of the multiplicand (11101)_{2}_{ }.

**Step 3: **Repeat the same process for all the next higher-order digits.

**Step 4: **The result after multiplication in each row is called partial product and final result will be the addition of all partial product.

(The binary bit addition rule is 0 + 0 = 0, 0 + 1 = 1, and 1 + 1 = 0, with a carryover of 1. And 1 + 1 = 10, 1 + 1 + 1 = 11 in binary system)

Below the figure described the binary bit multiplication.

Therefore, the product of (11101)_{2}_{ }and (1001)_{2}_{ }is (100000101)_{2}_{ }. Let us verify our answer. The decimal equivalent of (100000101)_{2}_{ }is 261. The decimal equivalent of (11101)_{2}_{ }is 29 and the decimal equivalent of (1001)_{2}_{ }is 9. We know in decimal the product of 29 and 9 is 261. The decimal equivalent of (100000101)_{2}_{ }is 261. Hence, the product is correct.

## Some Examples of Binary Multiplications

For batter understanding the concept of multiplication practice the given examples.

**Example 1: **Using the multiplications rules, multiply binary bits numbers (110)_{2 }and (11)_{2 }.

**Solution:**

The rules for binary multiplication are:

0 × 0 = 0

0 × 1 = 0

1 × 0 = 0

1 × 1 = 1

Use the above rule of binary multiplication. Given, multiplicand = (110)_{2 }, multiplier = (11)_{2 }. The multiplications of these two binary bits is described below.

Therefore, the product of (110)_{2}_{ }_{ }and (11)_{2}_{ }_{ }is (10010)_{2}_{ }_{ }

Comparison with Decimal values:

(110)_{2}_{ }_{ }= 6_{10}

(11)_{2}_{ } = 3_{10}

6 x 3 = 18_{10}

(10010)_{2} = 18_{10}

The example of binary multiplication with a decimal point is as follows:

**Question:** (1011.01)_{2}_{ }_{ } × (110.1)_{2}_{ }_{ }

**Solution:**

The position of decimal is placed after three binary bits because the binary number 1011.11, the decimal point is two from LSB and another binary number is 110.1, the decimal point placed is 1 from LSB.

### Multiplication Questions

Solve the given question using multiplication rule.

- Find the answer of this multiplication 10001 x 111
- Find out the multination result of given binary number 10101 x 110
- Evaluate 11111 x 10000

also read:- Binary addition, Binary subtraction, Binary division.

### Frequently Asked Questions

#### What is Binary Multiplications?

Binary multiplication is the one of the type of binary asthmatic operation in binary multiplication process involves addition and substation also. In multiplication only involve two bit and that bit are “0” and “1”

#### What are the Rules of Binary Multiplications?

There are four rules of multiplication which are:

- 0 × 0 = 0
- 0 × 1 = 0
- 1 × 0 = 0
- 1 × 1 = 1

#### How to do binary multiplications?

To solve multiplications problems based on binary numbers, we have to use the four primary rules designated for this operation. For example, if we have to multiply 110 by 100, then we get;

#### What are the steps for binary multiplications?

The process of multiplication is much similar to the decimal type of multiplication. First we need to multiply each digits of one binary number to each digit of another binary number. The result will be obtained by addition of bits.

#### What is the binary product of 1001 and 1011?

The binary product of (1001)_{2}_{ }_{ } and (1011)_{2}_{ }_{ } is (1100011)_{2}_{ }_{ }.