Convert Binary to Decimal - Fast & Accurate Binary ⇄ Decimal Converter

Need a quick way to convert binary to decimal or decimal to binary? Our Binary ⇄ Decimal converter gives instant and accurate results. Just enter the value and see the exact conversion anytime.

Why Users Love This Binary ⇄ Decimal Converter

• Accurate formulas: Uses the correct base-2 and base-10 methods.
• Instant calculation: Results appear as soon as you type.
• Clear results: Shows both detailed steps and final values.
• Two-way conversion: Works for both binary to decimal and decimal to binary.
• Easy access: Mobile and desktop friendly.

How to Use Our Converter

1. Enter your number.
2. Select the direction: Binary to Decimal or Decimal to Binary.
3. View the instant conversion.
4. Copy, share, or save the answer.

Binary Numbers

The term Binary refers to the base-2 number system. It only uses two digits: 0 and 1. Binary numbers are the foundation of computing because digital circuits understand only two states: ON (1) and OFF (0).

Key Facts About Binary

• Exact value: Each digit represents a power of 2.
• Relationship to Decimal: Binary is converted to Decimal by adding powers of 2.
• Common abbreviation: Bin or base-2.
• Notation tips: Always written with digits 0 and 1.

Decimal Numbers

The Decimal system is the base-10 number system. It uses digits from 0 to 9 and is the most common way humans represent numbers in daily life.

Key Facts About Decimal

• Exact value: Each digit represents a power of 10.
• Relationship to Binary: Decimal values can be converted into Binary using repeated division by 2.
• Common abbreviation: Dec or base-10.
• Notation tips: Used for counting, money, measurement, and arithmetic.

Binary to Decimal Conversion Formula

Formula:

Decimal = (bn × 2ⁿ) + (bn-1 × 2ⁿ⁻¹) + … + (b1 × 2¹) + (b0 × 2⁰)

Binary to Decimal Conversion Examples

Example 1: Convert 1011 to Decimal

• Step 1: Formula = (1 × 2³) + (0 × 2²) + (1 × 2¹) + (1 × 2⁰)
• Step 2: Substitute = 8 + 0 + 2 + 1
• Step 3: Result = 11

Example 2: Convert 11010 to Decimal

• Step 1: Formula = (1 × 2⁴) + (1 × 2³) + (0 × 2²) + (1 × 2¹) + (0 × 2⁰)
• Step 2: Substitute = 16 + 8 + 0 + 2 + 0
• Step 3: Result = 26

Example 3: Convert 111111 to Decimal

• Step 1: Formula = (1 × 2⁵) + (1 × 2⁴) + (1 × 2³) + (1 × 2²) + (1 × 2¹) + (1 × 2⁰)
• Step 2: Substitute = 32 + 16 + 8 + 4 + 2 + 1
• Step 3: Result = 63

Decimal to Binary Conversion Formula

Formula:

Binary = Divide Decimal by 2 and record remainders until quotient = 0.

Decimal to Binary Conversion Examples

Example 1: Convert 13 to Binary

• Step 1: 13 ÷ 2 = 6 remainder 1
• Step 2: 6 ÷ 2 = 3 remainder 0
• Step 3: 3 ÷ 2 = 1 remainder 1
• Step 4: 1 ÷ 2 = 0 remainder 1
• Result = 1101

Example 2: Convert 20 to Binary

• Step 1: 20 ÷ 2 = 10 remainder 0
• Step 2: 10 ÷ 2 = 5 remainder 0
• Step 3: 5 ÷ 2 = 2 remainder 1
• Step 4: 2 ÷ 2 = 1 remainder 0
• Step 5: 1 ÷ 2 = 0 remainder 1
• Result = 10100

Example 3: Convert 45 to Binary

• Step 1: 45 ÷ 2 = 22 remainder 1
• Step 2: 22 ÷ 2 = 11 remainder 0
• Step 3: 11 ÷ 2 = 5 remainder 1
• Step 4: 5 ÷ 2 = 2 remainder 1
• Step 5: 2 ÷ 2 = 1 remainder 0
• Step 6: 1 ÷ 2 = 0 remainder 1
• Result = 101101

Applications of Binary and Decimal Conversions

• Computer programming: Converting binary instructions into human-readable numbers.
• Networking: IP addressing often involves binary and decimal formats.
• Digital electronics: Binary is used in circuits, while Decimal is used for display.
• Mathematics & education: Understanding number systems for coding and problem solving.

Quick Reference Table for Binary ⇄ Decimal Conversion

Use our Binary ⇄ Decimal converter at Digital Calculator for fast, accurate, and reliable results in computer science, mathematics, and digital electronics.

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