Decimal to Binary Converter

To use decimal to binary converter, type a decimal value e.g. "16" and click on the Convert button and you will get the binary value "00010000" on the right hand side.

Decimal to Binary Conversion:

• Decimal Numeral System
• Binary Numeral System
• How to Convert Decimal to Binary
• How to Convert Fractional Decimal to Binary
• Decimal to Binary Examples
• FAQs (Decimal to Binary Conversion)
• Decimal to Binary Table

Decimal Numeral System

The decimal system is built on base 10, meaning it relies on ten unique digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Each position of a digit in a decimal number represents a power of 10, moving from left to right for whole numbers (10⁰, 10¹, 10², etc.) and right to left for fractional values (10^-1, 10^-2, etc.). This positional notation is what allows us to represent very large or very small values efficiently.

Example:

Consider the decimal number "3047.82" in the decimal system.

Total = (3 × 10³) + (0 × 10²) + (4 × 10¹) + (7 × 10⁰) + (8 × 10^-1) + (2 × 10^-2) = 3000 + 40 + 7 + 0.8 + 0.02 = 3047.82

Binary Numeral System

The binary number system is a base-2 numeral system that uses only two symbols: 0 and 1 and each symbol is also called as 1 bit. Each position in a binary number represents a power of 2, instead of 10 (as in decimal). The rightmost digit is 2⁰ (ones place), the next is 2¹ (twos place), then 2² (fours place), and so on. Binary is fundamental in computing because digital circuits operate with two states: on (1) and off (0).

Example:

Consider the binary number "1011.01", it can be expressed as:

Therefore (1110)₂ = (1 × 2³) + (0 × 2²) + (1 × 2¹) + (1 × 2⁰) + (0 × 2^-1) + (1 × 2^-2) = (8 + 2 + 1 + 0.25) = (11.25)₁₀ (Decimal)

How to Convert Decimal to Binary

Consider the following steps to convert a decimal number to a binary number:

• Step-1: Given the decimal number, repeatedly divide it by 2 until the quotient value is 0. If the quotient is not 0, then keep on dividing it by 2.

• Step-2: Get the remainder value from every step and it represents the bit value of the binary number.

• Step-3: Combine together all the remainder values to get the final binary value.

How to Convert Fractional Decimal Part to Binary Number

Follow these steps to convert fractional decimal value to binary:

• Step-1: Fetch the fractional part only from the number e.g. 0.75

• Step-2: Multiply it by 2 and after that record the integer value (e.g 1.5). This is the bit value at position 2^-1 i.e "1".

• Step-3: Take the fractional remainder value i.e "0.5" and continue with the step-2 until the fractional remainder value is 0.

• Step-4: After multiplying by 2, the subsequent interger values will represent the bits position 2^-2, 2^-3 and so on.

Decimal to Binary Examples

Example 1: Convert decimal number 9 to a binary value.

Example 2: Convert decimal number 184 to a binary value.

Example 3: Convert 1678 to a binary value.

Example 4: Convert 734.75 to a binary value.

Example 5: Convert 750.375 to a binary value.

Frequently Ask Questions: Decimal to Binary Conversion

Q1: Why do some decimal fractions (like 0.1) not convert exactly into binary?

Because binary is base-2, and some fractions in base-10 require infinite repeating bits in base-2 (just like 1/3 = 0.333... in decimal). The value of 0.1 decimal in binary is converted to (0.0001100110011001101)₂.

Q2: How do you verify that your decimal to binary conversion is correct?

Multiply each binary digit by its positional value (2ⁿ for integers, 2^-n for fractions) and sum them back to get the original decimal.

Q3: What are the binary equivalents of common decimal fractions values like 0.5, 0.25, 0.75?

(0.5)₁₀ = (0.1)₂ , (0.25)₁₀ = (0.01)₂ , (0.75)₁₀ = (0.11)₂

Q4: What is the shortcut to convert a decimal number that is a power of 2 into binary?

Write 1 followed by the same number of zeros as the exponent value. For example, the decimal value (32)₁₀ = 2⁵ = (100000)₂. Similarly, (128)₁₀ = 2⁷ = (10000000)₂

Q5: Why is decimal to binary conversion so important in computers?

Ccomputers store and process all data using base-2 (series of 1s and 0s). This binary data is stores in temporary and permanent memory locations e.g. RAM, Hard Drives, SSDs etc.

Decimal to Binary Table

by Wasim Khan and it was last modified on August 16, 2025

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