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About Binary to Decimal Converter with Steps – Step-by-Step Calculator

Convert binary numbers (base-2) into decimal values (base-10) with an educational step-by-step breakdown.

Inspect positional powers of 2, polynomial expansion formulas, bit contribution tables, and hexadecimal representations.

Input is processed locally in your browser and is not sent to Navorika.

Each binary digit d at position n (from right, 0-indexed) represents d × 2^n in base 10.

The total decimal value equals the sum of all active bit weights: Value = ∑ (b_i × 2^i) for i from 0 to N-1.

1Enter a binary number (e.g. 101101) or choose a sample value.
2Review the evaluated decimal result computed using BigInt arbitrary-precision arithmetic.
3Examine the step-by-step polynomial expansion formula and evaluated powers of 2.
4Inspect the positional bit breakdown table showing the weight and contribution of each bit.

Bits set to 1 add their positional power of 2 (1, 2, 4, 8, 16, 32...) to the decimal total.

Bits set to 0 contribute zero to the final summation.

Fractional binary values (e.g. 101.101) are not covered; this tool focuses on integer representations.
Inputs with thousands of bits are calculated accurately via BigInt but formulas are abbreviated for display.

How is 101101 converted to decimal?

101101₂ = 1×2⁵ + 0×2⁴ + 1×2³ + 1×2² + 0×2¹ + 1×2⁰ = 32 + 0 + 8 + 4 + 0 + 1 = 45.

Does this calculator handle large binary numbers?

Yes. The calculation engine uses JavaScript BigInt to prevent 53-bit floating-point precision loss.

Can I include spaces or the 0b prefix in my input?

Yes. Visual separators like spaces, underscores, and standard 0b prefixes are automatically stripped.

Selected from curated relationships first, then the same subtopic and category.

Bit Position	Binary Digit	Power of 2	Decimal Weight	Term Calculation	Contribution
2^5	1	2^5	32	1 × 32	32
2^4	0	2^4	16	0 × 16	0
2^3	1	2^3	8	1 × 8	8
2^2	1	2^2	4	1 × 4	4
2^1	0	2^1	2	0 × 2	0
2^0	1	2^0	1	1 × 1	1