Binary Converter
Convert binary numbers (base-2) to decimal, octal, hexadecimal, and any custom base. Perfect for computer science students and programmers working with binary data.
Binary Number Converter
Convert binary numbers (base-2) to decimal, octal, hexadecimal, and any custom base.
Binary (Base-2)
Only 0 and 1 are allowed
Result will appear here
Binary to Decimal Conversion
Conversion Method:
Base 2 to Decimal: Use positional notation
Formula:
Each digit × (base)^position, then sum all values
Examples with Step-by-Step Solutions
Example 1:
(1010)2
=
(10)10
Step-by-Step Solution:
Converting 1010₍2₎ to base 10:
Step 1: Convert Binary to decimal
1010₍2₎ = 1 × 2³ = 1 × 8 = 8 + 0 × 2² = 0 × 4 = 0 + 1 × 2¹ = 1 × 2 = 2 + 0 × 2⁰ = 0 × 1 = 0
= 8 + 0 + 2 + 0
= 10₁₀
Therefore: 1010₍2₎ = 10₁₀
Example 2:
(11011)2
=
(27)10
Step-by-Step Solution:
Converting 11011₍2₎ to base 10:
Step 1: Convert Binary to decimal
11011₍2₎ = 1 × 2⁴ = 1 × 16 = 16 + 1 × 2³ = 1 × 8 = 8 + 0 × 2² = 0 × 4 = 0 + 1 × 2¹ = 1 × 2 = 2 + 1 × 2⁰ = 1 × 1 = 1
= 16 + 8 + 0 + 2 + 1
= 27₁₀
Therefore: 11011₍2₎ = 27₁₀
Example 3:
(101101)2
=
(45)10
Step-by-Step Solution:
Converting 101101₍2₎ to base 10:
Step 1: Convert Binary to decimal
101101₍2₎ = 1 × 2⁵ = 1 × 32 = 32 + 0 × 2⁴ = 0 × 16 = 0 + 1 × 2³ = 1 × 8 = 8 + 1 × 2² = 1 × 4 = 4 + 0 × 2¹ = 0 × 2 = 0 + 1 × 2⁰ = 1 × 1 = 1
= 32 + 0 + 8 + 4 + 0 + 1
= 45₁₀
Therefore: 101101₍2₎ = 45₁₀
Example 4:
(11101001)2
=
(233)10
Step-by-Step Solution:
Converting 11101001₍2₎ to base 10:
Step 1: Convert Binary to decimal
11101001₍2₎ = 1 × 2⁷ = 1 × 128 = 128 + 1 × 2⁶ = 1 × 64 = 64 + 1 × 2⁵ = 1 × 32 = 32 + 0 × 2⁴ = 0 × 16 = 0 + 1 × 2³ = 1 × 8 = 8 + 0 × 2² = 0 × 4 = 0 + 0 × 2¹ = 0 × 2 = 0 + 1 × 2⁰ = 1 × 1 = 1
= 128 + 64 + 32 + 0 + 8 + 0 + 0 + 1
= 233₁₀
Therefore: 11101001₍2₎ = 233₁₀