Decimal to Binary Conversion - Fast & Accurate Converter

Need a fast and accurate way for decimal to binary conversion or the reverse? Our decimal ⇄ binary converter gives instant results. Just enter the value and get precise answers for decimal to binary and binary to decimal anytime.

Why Users Love This Decimal ⇄ Binary Converter

• Exact in design: Uses correct formulas for accurate results
• Instant answers: Get results as you type.
• Clear display: Shows exact and step-by-step conversions.
• Two-way switch: Convert decimal to binary or binary to decimal.
• Works anywhere: Mobile and desktop-friendly.

How to Use Our Converter

1. Enter the decimal or binary value.
2. Choose conversion direction: decimal to binary or binary to decimal.
3. View instant results.
4. Copy, share, or save the answer.

Decimal (Base-10)

The term decimal stands for the number system with base-10. It uses digits 0–9 and is the standard system we use in daily life for counting, arithmetic, and financial calculations.

Key Facts About Decimal

• Exact value: Each digit’s place value increases by powers of 10.
• Relationship to other systems: Can be converted to binary, octal, or hexadecimal.
• Common abbreviation: “Dec” or base-10.
• Notation tips: Always written with digits 0 to 9 only.

Binary (Base-2)

The term binary stands for the number system with base-2. It uses only two digits: 0 and 1. Binary is the language of computers, where every bit represents an electrical state (on = 1, off = 0).

Key Facts About Binary

• Exact value: Each digit’s place value increases by powers of 2.
• Relationship to other systems: Easily converted into decimal, hexadecimal, and octal.
• Common abbreviation: “Bin” or base-2.
• Notation tips: Written using only 0s and 1s.

Decimal to Binary Conversion Formula

Formula:

Binary = Divide decimal number by 2 and record remainders until quotient = 0. Read remainders from bottom to top.

Decimal to Binary Conversion Examples

Example 1: Convert 10 decimal to binary

• Step 1: Divide 10 ÷ 2 = 5 remainder 0
• Step 2: Divide 5 ÷ 2 = 2 remainder 1
• Step 3: Divide 2 ÷ 2 = 1 remainder 0
• Step 4: Divide 1 ÷ 2 = 0 remainder 1
• Result = 1010 binary

Example 2: Convert 25 decimal to binary

• Step 1: 25 ÷ 2 = 12 remainder 1
• Step 2: 12 ÷ 2 = 6 remainder 0
• Step 3: 6 ÷ 2 = 3 remainder 0
• Step 4: 3 ÷ 2 = 1 remainder 1
• Step 5: 1 ÷ 2 = 0 remainder 1
• Result = 11001 binary

Example 3: Convert 100 decimal to binary

• Step 1: 100 ÷ 2 = 50 remainder 0
• Step 2: 50 ÷ 2 = 25 remainder 0
• Step 3: 25 ÷ 2 = 12 remainder 1
• Step 4: 12 ÷ 2 = 6 remainder 0
• Step 5: 6 ÷ 2 = 3 remainder 0
• Step 6: 3 ÷ 2 = 1 remainder 1
• Step 7: 1 ÷ 2 = 0 remainder 1
• Result = 1100100 binary

Binary to Decimal Conversion Formula

Formula:

Decimal = Sum of (binary digit × 2^position).

Binary to Decimal Conversion Examples

Example 1: Convert 1010 binary to decimal
= (1 × 2³) + (0 × 2²) + (1 × 2¹) + (0 × 2⁰)
= 8 + 0 + 2 + 0
= 10 decimal

Example 2: Convert 11001 binary to decimal
= (1 × 2⁴) + (1 × 2³) + (0 × 2²) + (0 × 2¹) + (1 × 2⁰)
= 16 + 8 + 0 + 0 + 1
= 25 decimal

Example 3: Convert 1100100 binary to decimal
= (1 × 2⁶) + (1 × 2⁵) + (0 × 2⁴) + (0 × 2³) + (1 × 2²) + (0 × 2¹) + (0 × 2⁰)
= 64 + 32 + 0 + 0 + 4 + 0 + 0
= 100 decimal

Applications of Decimal and Binary Conversions

• Computer Science: Data representation in programming.
• Digital Electronics: Circuit design and logic gates.
• Networking: IP addressing uses binary.
• Storage Systems: File size representation in bits and bytes.

Quick Reference Table for Decimal ⇄ Binary Conversion

Use our decimal ⇄ binary converter at Digital Calculator for fast, accurate, and reliable results in computer science, programming, and everyday learning.

Our Popular Number System Calculators 

Decimal To Hex Converter

Hex To Decimal Converter

Binary To Hex Converter

Hex To Binary Converter

Binary To Octal Converter