Binary to Decimal Converter | Online & Free Web Based Tool

Binary to Decimal Converter

Convert to Decimal

About Binary

Binary, or base-2, is a numerical system that uses only two digits: 0 and 1. It is fundamental in computing and digital systems, where each binary digit, or bit, represents an off or on state, respectively. Binary numbers are used in various applications, including data encoding, computer processors, and digital circuits. Understanding binary is crucial for those interested in computer science, electronics, and information technology.

About Decimal

Decimal, or base-10, is the standard numerical system used by most people and is based on ten digits: 0 through 9. It is the foundation for arithmetic operations in everyday life, financial transactions, and various scientific calculations. The decimal system’s place value concept allows easy manipulation of large numbers and fractions. Mastery of decimal numbers is essential for mathematics, engineering, finance, and many scientific fields.

Conversion Examples

Binary	Decimal	Calculation Steps
1101	13	(1 × 2³) + (1 × 2²) + (0 × 2¹) + (1 × 2⁰) = 8 + 4 + 0 + 1 = 13
10101	21	(1 × 2⁴) + (0 × 2³) + (1 × 2²) + (0 × 2¹) + (1 × 2⁰) = 16 + 0 + 4 + 0 + 1 = 21
1110	14	(1 × 2³) + (1 × 2²) + (1 × 2¹) + (0 × 2⁰) = 8 + 4 + 2 + 0 = 14
10010	18	(1 × 2⁴) + (0 × 2³) + (0 × 2²) + (1 × 2¹) + (0 × 2⁰) = 16 + 0 + 0 + 2 + 0 = 18
110011	51	(1 × 2⁵) + (1 × 2⁴) + (0 × 2³) + (0 × 2²) + (1 × 2¹) + (1 × 2⁰) = 32 + 16 + 0 + 0 + 2 + 1 = 51

Binary to Decimal Conversion Table

Binary	Decimal
0000 0000	0
0000 0001	1
0000 0010	2
0000 0011	3
0000 0100	4
0000 0101	5
0000 0110	6
0000 0111	7
0000 1000	8
0000 1001	9
0000 1010	10
0000 1011	11
0000 1100	12
0000 1101	13
0000 1110	14
0000 1111	15
0001 0000	16
0001 0001	17
0001 0010	18
0001 0011	19
0001 0100	20