Conversions

Binary to Decimal Converter

Last updated: March 20, 2026

How to Use This Calculator

Step 1: Select Binary→Decimal or Decimal→Binary.

Step 2: Enter your number (binary: 0s and 1s only).

Step 3: Click Calculate for result plus hex equivalent.

Step 4: Review positional math breakdown.

What Is Binary?

Binary (base-2) is how computers store data — sequences of 0s and 1s. Each bit = on/off state. Decimal (base-10) uses digits 0-9.

Conversion uses positional notation. Each position = power of 2: 2⁰=1, 2¹=2, 2²=4, 2³=8. Binary 1101 = 8+4+0+1 = 13.

Conversion Formulas

Binary→Decimal: Multiply each digit by 2^position, sum.
11010110 = 128+64+16+4+2 = 214

Decimal→Binary: Divide by 2, record remainders bottom-up.
214: remainders 0,1,1,0,1,0,1,1 → 11010110

Reference Table

Binary	Decimal	Hex
0001	1	1
0010	2	2
0100	4	4
1000	8	8
1010	10	A
1111	15	F
10000	16	10
11111111	255	FF

Examples

Example 1: 10110 = 16+4+2 = 22

Example 2: 11111111 = 255 (max byte)

Example 3: 42 decimal = 101010 binary

Binary Tips

Key powers of 2: 2⁸=256, 2¹⁰=1024, 2¹⁶=65536.

Group in 4s for hex: 1101 0110 = D6.

8 bits = 0-255. Max of N bits = 2ᴺ-1.

Useful for networking — IP addresses and subnet masks.

Frequently Asked Questions

What is the largest binary number I can convert?

This calculator handles binary numbers up to 53 bits, which equals 9,007,199,254,740,991 in decimal. This limit comes from JavaScript's number precision. For practical purposes, this covers everything from basic computer science homework to networking (32-bit IP addresses), file permissions, and most programming scenarios.

Why do computers use binary instead of decimal?

Computer processors are built from billions of transistors, each of which can be in one of two states: on (representing 1) or off (representing 0). Binary maps directly to these physical states, making it the most reliable and efficient number system for electronic circuits. Using 10 states (for decimal) would require much more complex circuitry and would be more prone to errors from electrical noise.

What is hexadecimal and why is it shown alongside decimal?

Hexadecimal (base-16) uses digits 0-9 and letters A-F to represent values 0-15. It is shown because each hex digit maps to exactly 4 binary digits, making it a compact shorthand for binary. Programmers prefer hex because it is much shorter — the 8-digit binary number 11111111 is just FF in hex. Memory addresses, color codes, and MAC addresses all use hexadecimal notation.

Can I convert binary fractions like 10.11?

This calculator handles whole numbers only. For binary fractions, digits after the binary point represent negative powers of 2. The first position after the point is 2 to the power of -1 (0.5), the second is 2 to the power of -2 (0.25), and so on. So binary 10.11 equals 2 + 0.5 + 0.25 = 2.75 in decimal. You would need to calculate this manually.

Can I convert negative numbers to binary?

This calculator works with non-negative integers (zero and positive whole numbers). In computing, negative binary numbers use a system called two's complement, where the leftmost bit indicates the sign. To properly interpret a negative binary number, you need to know the bit width (8-bit, 16-bit, or 32-bit), which determines the range of representable values.

What is the difference between binary and Boolean?

Binary is a complete number system (base-2) that can represent any quantity using multiple digits — like 11010 representing 26. Boolean is a logical system with only two possible values: true (1) and false (0). While both use 0 and 1, binary numbers can have any number of digits, whereas Boolean is always a single true-or-false value. Binary arithmetic and Boolean logic also follow different rules.

Binary Number

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Binary to Decimal Converter

How to Use This Calculator

What Is Binary?

Conversion Formulas

Reference Table

Examples

Binary Tips

Frequently Asked Questions

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