Binary To Decimal Formula

Decimal to Binary Formula

The Binary To Decimal Formula for converting decimal values to binary numbers is known as the decimal-to-binary conversion. The remainder formula makes it simple to translate decimal integers into binary numbers. The process involves recursively dividing the given decimal number by 2 while keeping track of the remainder until we arrive at a quotient of 0 or 1.

There are numerous methods for converting between binary and decimal. One method to convert a Binary To Decimal Formula number is to divide it by two recursively. The remaining amount is added until the quotient is finally equal to 0. The binary equivalent of the supplied decimal number is then created by writing these leftovers in reverse order. A number system is a way to represent numbers numerically using a collection of digits or symbols. Number representations exist, with some examples being the decimal, binary, octal, and hexadecimal number systems.

The Binary To Decimal Formula system is a base-2 number system where numbers are solely represented by the digits 0 and 1. A bit is the shorthand name for a “binary digit,” which is the smallest piece of data that can be stored in a computer. A bit only has one binary value, which can be either 1 or 0. Since computers only understand the binary digits 0 and 1, they are most often employed in programming and coding.

What is Decimal to Binary Formula?

In the Binary To Decimal Formula to convert a decimal number to binary, one must divide the given decimal number recursively by 2 and record the remainder until one has a final quotient of either 0 or 1.

Using the  Binary To Decimal Formula for converting from decimal to binary, the following steps are taken:

  • Step 1: Subtract 2 from the supplied decimal number and record the result.
  • Step 2: Next, divide the result of the previous step’s division by two, noting the remaining.
  • Step 3: Continue the previous steps until the quotient is either 0 or 1.
  • Step 4: As the binary conversion of the equation, write down the final quotient in line with the remainder going from last to first.

Solved Examples

Example 1: Using the Binary To Decimal Formula, convert 29 decimals into a binary number.


Using Binary To Decimal Formula, we have,

  • Step 1: Divide the number by 2, and note down the remainder:

29 ÷ 2 gives Q1Q1 = 14, R = 1

  • Step 2: Divide Q1Q1 by 2, and note down the remainder:

14 ÷ 2 gives Q2Q2 = 7, R = 0

  • Step 3: Divide Q2Q2 by 2, and note down the remainder:

7 ÷ 2 gives Q3Q3 = 3, R = 1

  • Step 4: Divide Q3Q3 by 2, and note down the remainder:

3 ÷ 2 gives Q4Q4 = 1, R = 1

  • Step 5: Write down the last quotient in line with the remainder from the last to the first. This is our binary conversion of the given decimal number:


Answer: Hence, 29 as binary is 111012111012.

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