Binary to Decimal Converter
Convert binary numbers to decimal. See step-by-step conversion process.
Binary: 1010
10
Decimal
Conversion Steps
| Bit | Position | 2^n | Value |
|---|---|---|---|
| 1 | 3 | 8 | 8 |
| 0 | 2 | 4 | 0 |
| 1 | 1 | 2 | 2 |
| 0 | 0 | 1 | 0 |
| Total | 10 | ||
Common Conversions
1
= 1
10
= 2
1010
= 10
11111111
= 255
How It Works
Binary is a base-2 number system using only 0 and 1. Each position represents a power of 2.
1010 (binary)
= 1×2³ + 0×2² + 1×2¹ + 0×2⁰
= 8 + 0 + 2 + 0
= 10 (decimal)
What Is Binary to Decimal Conversion?
Binary to decimal conversion translates numbers from the base 2 numeral system (binary) to the base 10 system (decimal) that humans use in everyday life. Binary uses only two digits — 0 and 1 — while decimal uses ten digits (0-9). Each position in a binary number represents a power of 2, starting from 2⁰ on the right. To convert, you multiply each binary digit by its corresponding power of 2 and sum the results.
This conversion is one of the most fundamental operations in computer science. Every piece of data stored in a computer exists as binary, but humans need to understand these values in decimal form. Whether you are reading memory addresses, interpreting network configurations, debugging programs, or studying computer architecture, the ability to convert between binary and decimal is an essential skill.
This converter provides both the final decimal result and a detailed step-by-step breakdown showing how each bit contributes to the total value. The conversion table displays the position, power of 2, and computed value for every bit, making it easy to understand the process and verify the result.
The Binary to Decimal Formula
Each bit in a binary number contributes a value equal to itself multiplied by 2 raised to the power of its position. The positions are numbered from right to left, starting at 0.
Binary to Decimal Conversion
Where:
- bit_i= The binary digit (0 or 1) at position i
- 2^i= The weight of position i (1, 2, 4, 8, 16, ...)
- n= Total number of bits in the binary number
Binary Position Weights
Understanding the weight of each bit position is the key to binary conversion. Each position doubles in weight as you move from right to left.
| Position | Power of 2 | Decimal Value |
|---|---|---|
| 0 | 2⁰ | 1 |
| 1 | 2¹ | 2 |
| 2 | 2² | 4 |
| 3 | 2³ | 8 |
| 4 | 2⁴ | 16 |
| 5 | 2⁵ | 32 |
| 6 | 2⁶ | 64 |
| 7 | 2⁷ | 128 |
How to Use This Calculator
The binary to decimal converter provides an interactive learning experience:
- Enter a binary number: Type any sequence of 0s and 1s into the input field. Invalid characters are automatically stripped from the input.
- View the decimal result: The converted decimal value appears instantly in the large result display.
- Examine the conversion steps: A detailed table shows each bit, its position, the power of 2, and the computed value. The total at the bottom confirms the final result.
- Try common values: Quick-select buttons provide pre-filled binary values for rapid exploration.
Invalid binary input (characters other than 0 and 1) is automatically filtered, and only valid binary digits contribute to the result.
Real-World Applications
Binary to decimal conversion is used daily in computer programming when debugging code, reading memory dumps, or interpreting raw data. A developer examining a core dump might see the hex value 0x1A3F, which is 0001101000111111 in binary and 6,719 in decimal. Quick conversion between these representations helps identify data values, memory addresses, and flag bits.
In networking, understanding binary conversion is essential for working with IP addresses and subnet masks. A subnet mask of 255.255.255.128 in decimal corresponds to 11111111.11111111.11111111.10000000 in binary, revealing that the first 25 bits form the network portion and the remaining 7 bits are for host addresses. This binary perspective is necessary for calculating network ranges and CIDR notation.
Embedded systems and IoT development require binary conversion when configuring hardware registers, setting bit flags, and programming microcontroller peripherals. Each bit in a control register might enable or disable a specific feature, and understanding the decimal equivalent of bit patterns helps developers write correct configuration code.
Worked Examples
Basic Binary to Decimal Conversion
Problem:
Convert the binary number 1010 to decimal.
Solution Steps:
- 1Write out each bit with its position: 1(3) 0(2) 1(1) 0(0)
- 2Calculate each bit's contribution: 1×2³ + 0×2² + 1×2¹ + 0×2⁰
- 3Compute: 8 + 0 + 2 + 0 = 10
Result:
1010 in binary = 10 in decimal
Converting an 8-bit Binary Number
Problem:
Convert the binary number 11010110 to decimal.
Solution Steps:
- 1Write out each bit with its position: 1(7) 1(6) 0(5) 1(4) 0(3) 1(2) 1(1) 0(0)
- 2Calculate each bit's contribution: 128 + 64 + 0 + 16 + 0 + 4 + 2 + 0
- 3Sum: 128 + 64 + 16 + 4 + 2 = 214
Result:
11010110 in binary = 214 in decimal
Converting a Large Binary Number
Problem:
What is the decimal equivalent of binary 11111111?
Solution Steps:
- 1All 8 bits are 1, so sum all powers of 2 from 2⁰ to 2⁷
- 2Sum: 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 = 255
- 3Alternatively: 2⁸ - 1 = 256 - 1 = 255
Result:
11111111 in binary = 255 in decimal (maximum 8-bit unsigned value)
Tips & Best Practices
- ✓Memorize the first 12 powers of 2 for instant binary-to-decimal conversion in your head
- ✓All 1s in binary means the maximum value: 8 bits of 1s = 255, 16 bits of 1s = 65,535
- ✓Each additional binary digit doubles the range of representable values
- ✓Binary numbers with a 1 in the highest position are always odd if the lowest bit is 1
- ✓Use the step-by-step table to verify your manual calculations
- ✓Common pattern: 1000 = 8, 10000 = 16, 100000 = 32 — just one 1 followed by zeros
Frequently Asked Questions
Sources & References
Last updated: 2026-06-06
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Editorial Note
MyCalcBuddy Editorial Team
This page is maintained as an educational calculator reference.
Formula Source: NIST Guide to SI Units
by National Institute of Standards