二进制转十进制转换器

How to Convert Binary to Decimal

Converting binary to decimal uses positional notation, the same principle behind every number system. Each digit in a binary number represents a power of 2, just as each digit in a decimal number represents a power of 10. Because binary is base-2 and has only two symbols (0 and 1), each bit position doubles in value from right to left: 1, 2, 4, 8, 16, 32, 64, 128, and so on.

Step-by-Step Positional Notation Method

The Double Dabble Method

The Double Dabble method (also known as the doubling method) is a mental arithmetic shortcut that avoids calculating large powers of 2. Instead of multiplying each bit by its power and summing, you process the binary number from left to right using a simple rule: double the running total and add the current bit.

Double Dabble Example: 11010 to Decimal

Double Dabble Example: 10110011 to Decimal

The Double Dabble method is particularly useful for converting long binary numbers by hand, since you never need to remember large powers of 2. It works because doubling the running total is equivalent to shifting all previous bits one position left (multiplying by 2) before adding the next bit.

Binary to Decimal Conversion Examples

Convert 1010 to Decimal

Convert 11111111 to Decimal

Convert 10000000 to Decimal

Convert 1100100 to Decimal

Binary to Decimal Conversion Table

This complete binary to decimal conversion table covers all 256 byte values from 0 to 255. Each row shows the decimal value, its 8-bit binary representation, hexadecimal equivalent, and octal representation.

Quick Reference (Powers of 2 & Common Values):

This table covers all possible single-byte values (0-255) with their binary, hexadecimal, and octal equivalents. For values beyond 255, apply the same positional notation method to larger binary numbers.

Signed Binary & Two's Complement

Unsigned binary can only represent non-negative numbers. To represent negative numbers, computers use two's complement, the standard signed binary system used by virtually all modern processors.

How Two's Complement Works

In two's complement, the most significant bit (MSB) is the sign bit: 0 means positive, 1 means negative. The remaining bits hold the magnitude, but negative values are encoded by inverting all bits and adding 1.

Two's Complement Range

Binary Fractions to Decimal

Binary numbers can have a fractional part, separated by a binary point (similar to a decimal point). Bits after the binary point represent negative powers of 2: 2^-1 = 0.5, 2^-2 = 0.25, 2^-3 = 0.125, and so on.

Example: Convert 101.11 to Decimal

Example: Convert 1.0101 to Decimal

Note: Some decimal fractions cannot be represented exactly in binary (for example, 0.1 in decimal is a repeating fraction in binary: 0.0001100110011...). This is why floating-point arithmetic can produce small rounding errors in programming.

Binary to Decimal in Programming

Most programming languages provide built-in functions for converting binary strings to decimal integers. Here are examples in the three most commonly used languages.

Python

# Convert binary string to decimal
binary_str = "10110011"
decimal_value = int(binary_str, 2)
print(decimal_value)          # 179

# Binary literal in Python
x = 0b10110011
print(x)                      # 179

# Convert decimal back to binary
print(bin(179))               # '0b10110011'

# Two's complement for signed 8-bit
def signed_binary_to_decimal(binary_str, bits=8):
    value = int(binary_str, 2)
    if value >= 2**(bits - 1):
        value -= 2**bits
    return value

print(signed_binary_to_decimal("11111001"))  # -7
print(signed_binary_to_decimal("01111111"))  # 127

JavaScript

// Convert binary string to decimal
const binaryStr = "10110011";
const decimal = parseInt(binaryStr, 2);
console.log(decimal);           // 179

// Binary literal in JavaScript
const x = 0b10110011;
console.log(x);                 // 179

// Convert decimal back to binary
console.log((179).toString(2)); // '10110011'

// For large binary values, use BigInt
const bigBin = "1111111111111111111111111111111111111111";
const bigDec = BigInt("0b" + bigBin);
console.log(bigDec.toString()); // '1099511627775'

C

#include <stdio.h>
#include <string.h>
#include <math.h>

long binaryToDecimal(const char *binary) {
    long decimal = 0;
    int len = strlen(binary);
    for (int i = 0; i < len; i++) {
        if (binary[i] == '1') {
            decimal += (long)pow(2, len - 1 - i);
        }
    }
    return decimal;
}

int main() {
    printf("%ld\n", binaryToDecimal("10110011")); // 179
    printf("%ld\n", binaryToDecimal("11111111")); // 255
    printf("%ld\n", binaryToDecimal("1100100"));  // 100

    // C also supports binary literals (C23/GCC extension)
    // int x = 0b10110011;  // 179
    return 0;
}

Applications

• Computer architecture: Understanding how CPUs process data at the binary level and convert to human-readable decimal output
• Networking: IP address and subnet mask calculations require binary-to-decimal conversion (e.g., subnet mask 11111111.11111111.11111111.00000000 = 255.255.255.0)
• Digital electronics: Reading sensor outputs, ADC (Analog-to-Digital Converter) values, and logic gate states
• Programming: Bitwise operations, bit flags, permissions, and debugging binary data
• Data encoding: Understanding character encodings like ASCII (7-bit) and UTF-8 (variable-length binary sequences)
• Cryptography: Binary operations underpin XOR encryption, hash functions, and block ciphers used in our Vernam cipher and other tools

Related Converters

Explore our other number system and encoding converters for related tasks:

• Hex to Binary Converter — Convert hexadecimal numbers to binary with 4-bit group visualization
• Binary to Octal Converter — Convert binary numbers to octal (base-8) using 3-bit grouping
• Binary Translator — Translate between binary and text (ASCII/Unicode) in both directions
• Hex to Decimal Converter — Convert hexadecimal values to decimal numbers
• ASCII Converter — Convert between ASCII characters and their numeric codes
• Base64 Encoder/Decoder — Encode and decode data in Base64 format

For an in-depth tutorial with multiple methods and code examples, read our comprehensive guide: How to Convert Binary to Decimal: 3 Methods with Examples & Code.