Table of Contents
What is Binary Multiplication?
Binary multiplication is a mathematical operation that is used to multiply two binary numbers together. The result of binary multiplication is a binary number that is the product of the two original numbers.
Decimal-To-Binary Conversion
To convert a decimal number to binary, divide the number by 2. If the result is a whole number, write the number down. If the result is a fraction, write down the numerator (top number) and place a slash (/) followed by the denominator (bottom number). Continue this process until you reach 0.
For example, to convert the decimal number 153 to binary, divide 153 by 2. The result is 76.5, which can written as 76/2. Write the number down and then divide it by 2 again. The result is 38.25, which can written as 38/2. Write the number down and then divide it by 2 again. The result is 19.125, which can written as 19/2. Write the number down and then divide it by 2 again. The result is 9.5625, which can be written as 9/2. Write the number down and then divide it by 2 again. The result is 4.78125, which can be written as 4/2. Write the number down and then divide it by 2 again. The result is 2.390625, which can be written as 2/2. The number 153 is now written as 11001011 in binary.
Steps to Convert an Integer to Binary
To convert an integer to binary, divide the number by 2 and take the remainder. Convert the remainder to binary and append it to the result of the previous division. Repeat the process until the number is 0.
Binary-To-Decimal Conversion
The number 11011 in binary is:
11011 = (1 x 2^3) + (1 x 2^2) + (0 x 2^1) + (1 x 2^0)
= (8) + (4) + (0) + (1)
= (13)
How to Do Binary Multiplication
To multiply two binary numbers, multiply the first number by the second number’s least significant bit, and add the products together.
For example, to multiply 11 by 101:
1 × 1 + 1 × 0 + 1 × 1 = 3
Steps to Multiply Binary Numbers
To multiply two binary numbers, follow these steps:
- Step 1: Write the numbers down in a column. The number on the left is the first number, and the number on the right is the second number.
- Step 2: Multiply each digit in the first number by the digit in the same position in the second number. Write the products down in the column.
- Step 3: Add the products together. The final number is the answer.
