Convert binary to decimal instantly with our professional binary to decimal converter. Features binary to decimal table, conversion examples in Python, Java, C++, and Excel formulas. Perfect binary to decimal calculator for programmers and students.
Master binary to decimal conversion with step-by-step examples, programming code samples, file processing methods, and comprehensive conversion tables. Supports all binary to decimal conversion scenarios from simple calculator operations to complex file transformations including 1011 binary to decimal, 1111 binary to decimal, and 10001 binary to decimal conversions.
The binary to decimal conversion formula uses positional notation where each binary digit is multiplied by 2 raised to the power of its position. This binary to decimal calculator method works because binary is a base-2 number system, making the conversion systematic and reliable.
Therefore, 1101 binary to decimal = 13
Essential binary to decimal table for manual calculations and programming reference.
| Binary | Decimal | Hex |
|---|---|---|
| 0000 | 0 | 0 |
| 0001 | 1 | 1 |
| 0010 | 2 | 2 |
| 0011 | 3 | 3 |
| 0100 | 4 | 4 |
| 0101 | 5 | 5 |
| 0110 | 6 | 6 |
| 0111 | 7 | 7 |
| 1000 | 8 | 8 |
| 1001 | 9 | 9 |
| 1010 | 10 | A |
| 1011 | 11 | B |
| 1100 | 12 | C |
| 1101 | 13 | D |
| 1110 | 14 | E |
| 1111 | 15 | F |
| Binary | Decimal | Description |
|---|---|---|
| 11111111 | 255 | 8-bit all 1s |
| 10000000 | 128 | 8-bit MSB |
| 01111111 | 127 | 8-bit max signed |
| 10101010 | 170 | Alternating pattern |
| 01010101 | 85 | Inverse alternating |
| 00001111 | 15 | Lower nibble |
| 11110000 | 240 | Upper nibble |
| 1111111111111111 | 65535 | 16-bit all 1s |
| 1000000000000000 | 32768 | 16-bit MSB |
| 1011101011101101 | 48109 | Complex pattern |
# Binary to Decimal Python - Method 1: Using int() function
binary_value = "1101"
decimal = int(binary_value, 2)
print(f"Binary to Decimal: {binary_value} = {decimal}")
# Output: Binary to Decimal: 1101 = 13
# Binary to Decimal Python - Method 2: Manual conversion
def binary_to_decimal_converter(binary_str):
decimal = 0
for i, bit in enumerate(binary_str[::-1]):
if bit == '1':
decimal += 2 ** i
return decimal
# Binary to Decimal conversion example
result = binary_to_decimal_converter("1101")
print(f"Binary to Decimal Result: 1101 = {result}")
# Binary to Decimal file processing
def convert_binary_file_to_decimal(input_file, output_file):
with open(input_file, 'r') as f:
binary_data = f.read().strip()
decimal_result = binary_to_decimal_converter(binary_data)
with open(output_file, 'w') as f:
f.write(str(decimal_result))
# Binary to Decimal list processing
def process_binary_list(binary_list):
return [int(binary, 2) for binary in binary_list]
binary_numbers = ["1011", "1111", "10001", "1010"]
decimal_numbers = process_binary_list(binary_numbers)
print("Binary to Decimal conversions:", decimal_numbers)
# Output: [11, 15, 17, 10]import java.util.*;
public class BinaryToDecimalConverter {
// Binary to Decimal Java - Method 1: Using Integer.parseInt()
public static int binaryToDecimal(String binary) {
return Integer.parseInt(binary, 2);
}
// Binary to Decimal Java - Method 2: Manual conversion
public static int binaryToDecimalManual(String binary) {
int decimal = 0;
int power = 0;
for (int i = binary.length() - 1; i >= 0; i--) {
if (binary.charAt(i) == '1') {
decimal += Math.pow(2, power);
}
power++;
}
return decimal;
}
// Binary to Decimal calculator example
public static void main(String[] args) {
String[] binaryNumbers = {"1011", "1111", "10001", "1010"};
System.out.println("Binary to Decimal Conversions:");
for (String binary : binaryNumbers) {
int decimal = binaryToDecimal(binary);
System.out.printf("%s binary to decimal = %d\n",
binary, decimal);
}
}
}#include <iostream>
#include <string>
#include <cmath>
#include <vector>
class BinaryToDecimalConverter {
public:
// Binary to Decimal C++ - Method 1: Using stoi()
static int binaryToDecimal(const std::string& binary) {
return std::stoi(binary, nullptr, 2);
}
// Binary to Decimal C++ - Method 2: Manual conversion
static int binaryToDecimalManual(const std::string& binary) {
int decimal = 0;
int power = 0;
for (int i = binary.length() - 1; i >= 0; i--) {
if (binary[i] == '1') {
decimal += std::pow(2, power);
}
power++;
}
return decimal;
}
};
// Binary to Decimal C++ calculator example
int main() {
std::vector<std::string> binaryNumbers =
{"1011", "1111", "10001", "1010"};
std::cout << "Binary to Decimal Conversions:\n";
for (const auto& binary : binaryNumbers) {
int result = BinaryToDecimalConverter::binaryToDecimal(binary);
std::cout << binary << " binary to decimal = "
<< result << std::endl;
}
return 0;
}// Binary to Decimal Excel Formula Examples
// Method 1: Using BIN2DEC function (for values up to 10 bits)
=BIN2DEC("1011")
// Result: 11
// Method 2: Manual formula for any length binary
// For cell A1 containing "1011", use this formula:
=SUMPRODUCT(MID(A1,ROW(INDIRECT("1:"&LEN(A1))),1)*
POWER(2,LEN(A1)-ROW(INDIRECT("1:"&LEN(A1)))))
// Binary to Decimal Excel table for reference:
// A1: Binary | B1: Decimal | Formula in B1: =BIN2DEC(A1)
// 1011 | 11 |
// 1111 | 15 |
// 10001 | 17 |
// 1010 | 10 |
// Excel VBA Function for binary to decimal conversion:
Function BinaryToDecimalConverter(binaryValue As String) As Long
Dim i As Integer
Dim decimalResult As Long
For i = 1 To Len(binaryValue)
If Mid(binaryValue, i, 1) = "1" Then
decimalResult = decimalResult + 2 ^ (Len(binaryValue) - i)
End If
Next i
BinaryToDecimalConverter = decimalResult
End Function
// Usage in Excel cell:
=BinaryToDecimalConverter("1011")
// Result: 11Embed our binary to decimal converter into your website or blog to provide your users with a convenient binary to decimal calculator tool. Perfect for educational sites, programming tutorials, and technical documentation.
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