Easily convert numbers between binary (base-2) and decimal (base-10) systems. Enter a binary number to get its decimal equivalent, or a decimal number to get its binary representation.
function convertToDecimal() {
var binaryInput = document.getElementById("binaryInput").value.trim();
var resultDiv = document.getElementById("result");
if (binaryInput === "") {
resultDiv.innerHTML = "Please enter a binary number.";
return;
}
// Validate if the input contains only 0s and 1s
if (!/^[01]+$/.test(binaryInput)) {
resultDiv.innerHTML = "Invalid binary number. Please use only 0s and 1s.";
return;
}
try {
var decimalValue = parseInt(binaryInput, 2);
resultDiv.innerHTML = "
" + decimalValue + "";
} catch (e) {
resultDiv.innerHTML = "Error converting binary to decimal. Please check your input.";
}
}
function convertToBinary() {
var decimalInput = document.getElementById("decimalInput").value.trim();
var resultDiv = document.getElementById("result");
if (decimalInput === "") {
resultDiv.innerHTML = "Please enter a decimal number.";
return;
}
var decimalNumber = parseInt(decimalInput, 10);
if (isNaN(decimalNumber) || decimalNumber < 0) {
resultDiv.innerHTML = "Invalid decimal number. Please enter a non-negative integer.";
return;
}
try {
var binaryValue = decimalNumber.toString(2);
resultDiv.innerHTML = "
" + binaryValue + "";
} catch (e) {
resultDiv.innerHTML = "Error converting decimal to binary. Please check your input.";
}
}
.binary-calculator-container {
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
background-color: #f9f9f9;
padding: 25px;
border-radius: 10px;
box-shadow: 0 4px 12px rgba(0, 0, 0, 0.1);
max-width: 600px;
margin: 30px auto;
border: 1px solid #e0e0e0;
}
.binary-calculator-container h2 {
color: #333;
text-align: center;
margin-bottom: 20px;
font-size: 26px;
}
.binary-calculator-container p {
color: #555;
line-height: 1.6;
margin-bottom: 15px;
text-align: center;
}
.calculator-form .form-group {
margin-bottom: 20px;
display: flex;
flex-wrap: wrap;
align-items: center;
gap: 10px;
}
.calculator-form label {
flex: 1 1 120px;
color: #333;
font-weight: bold;
font-size: 15px;
}
.calculator-form input[type="text"],
.calculator-form input[type="number"] {
flex: 2 1 200px;
padding: 12px;
border: 1px solid #ccc;
border-radius: 5px;
font-size: 16px;
transition: border-color 0.3s ease;
}
.calculator-form input[type="text"]:focus,
.calculator-form input[type="number"]:focus {
border-color: #007bff;
outline: none;
box-shadow: 0 0 5px rgba(0, 123, 255, 0.2);
}
.calculator-form button {
flex: 1 1 100px;
background-color: #007bff;
color: white;
padding: 12px 18px;
border: none;
border-radius: 5px;
cursor: pointer;
font-size: 16px;
transition: background-color 0.3s ease, transform 0.2s ease;
white-space: nowrap;
}
.calculator-form button:hover {
background-color: #0056b3;
transform: translateY(-1px);
}
.calculator-form button:active {
transform: translateY(0);
}
.result-container {
background-color: #e9f7ff;
border: 1px solid #b3e0ff;
padding: 15px 20px;
border-radius: 8px;
margin-top: 25px;
}
.result-container h3 {
color: #0056b3;
margin-top: 0;
margin-bottom: 10px;
font-size: 20px;
text-align: center;
}
.calculator-result p {
font-size: 18px;
color: #333;
margin: 8px 0;
text-align: left;
}
.calculator-result p strong {
color: #007bff;
}
@media (max-width: 480px) {
.calculator-form .form-group {
flex-direction: column;
align-items: stretch;
}
.calculator-form label,
.calculator-form input,
.calculator-form button {
flex: none;
width: 100%;
}
.calculator-form button {
margin-top: 10px;
}
}
Understanding Binary and Decimal Systems
The world around us primarily uses the decimal (base-10) number system, which employs ten unique digits (0-9). This system is intuitive for humans because we have ten fingers, making it a natural fit for counting.
However, computers operate fundamentally differently. They use the binary (base-2) number system, which consists of only two digits: 0 and 1. These digits represent the two states of electrical signals within a computer: 'off' (0) or 'on' (1). Every piece of data, from text and images to complex programs, is ultimately stored and processed as sequences of these binary digits, known as bits.
How Binary to Decimal Conversion Works
Converting a binary number to its decimal equivalent involves understanding place values. In the decimal system, each digit's position represents a power of 10 (e.g., 10^0 for the ones place, 10^1 for the tens place, 10^2 for the hundreds place, and so on). Similarly, in the binary system, each digit's position represents a power of 2.
To convert a binary number to decimal:
- Start from the rightmost digit (least significant bit).
- Multiply each digit by 2 raised to the power of its position (starting from 0 for the rightmost digit).
- Sum up all the results.
Example: Convert binary 10110 to decimal.
0 * 2^0 = 0 * 1 = 01 * 2^1 = 1 * 2 = 21 * 2^2 = 1 * 4 = 40 * 2^3 = 0 * 8 = 01 * 2^4 = 1 * 16 = 16
Summing these values: 0 + 2 + 4 + 0 + 16 = 22. So, binary 10110 is decimal 22.
How Decimal to Binary Conversion Works
Converting a decimal number to binary involves a process of repeated division by 2.
To convert a decimal number to binary:
- Divide the decimal number by 2.
- Note the remainder (which will be either 0 or 1).
- Take the quotient from the division and divide it by 2 again.
- Repeat this process until the quotient becomes 0.
- Write down the remainders in reverse order (from last to first) to get the binary number.
Example: Convert decimal 22 to binary.
22 / 2 = 11 remainder 011 / 2 = 5 remainder 15 / 2 = 2 remainder 12 / 2 = 1 remainder 01 / 2 = 0 remainder 1
Reading the remainders from bottom to top: 10110. So, decimal 22 is binary 10110.
Using the Binary Calculator
Our Binary & Decimal Converter simplifies these conversions. Simply enter your binary number into the "Binary Number" field and click "Convert to Decimal" to see its decimal equivalent. Alternatively, enter your decimal number into the "Decimal Number" field and click "Convert to Binary" to get its binary representation. The calculator handles the complex math, providing instant and accurate results, making it an invaluable tool for students, programmers, and anyone working with digital systems.