Calculator for Binary Numbers

Binary-Decimal Converter

function convertBinaryToDecimal() { var binaryString = document.getElementById("numberInput").value.trim(); var resultElement = document.getElementById("result"); if (binaryString === "") { resultElement.innerHTML = "Please enter a binary number."; return; } // Validate if it's a valid binary string (only '0' and '1') if (!/^[01]+$/.test(binaryString)) { resultElement.innerHTML = "Invalid binary number. Please use only '0's and '1's."; return; } try { var decimalValue = parseInt(binaryString, 2); resultElement.innerHTML = "Decimal: " + decimalValue; } catch (e) { resultElement.innerHTML = "Error converting binary to decimal. Please check your input."; } } function convertDecimalToBinary() { var decimalString = document.getElementById("numberInput").value.trim(); var resultElement = document.getElementById("result"); if (decimalString === "") { resultElement.innerHTML = "Please enter a decimal number."; return; } // Validate if it's a valid non-negative integer if (!/^\d+$/.test(decimalString)) { resultElement.innerHTML = "Invalid decimal number. Please enter a non-negative integer."; return; } var decimalValue = parseInt(decimalString, 10); if (isNaN(decimalValue) || decimalValue < 0) { resultElement.innerHTML = "Invalid decimal number. Please enter a non-negative integer."; return; } try { var binaryValue = decimalValue.toString(2); resultElement.innerHTML = "Binary: " + binaryValue; } catch (e) { resultElement.innerHTML = "Error converting decimal to binary. Please check your input."; } } function clearFields() { document.getElementById("numberInput").value = ""; document.getElementById("result").innerHTML = ""; }

Understanding Binary and Decimal Numbers

The world of computing relies heavily on binary numbers, a base-2 numeral system, while humans are most familiar with the decimal system, a base-10 system. This converter helps bridge the gap, allowing you to easily translate numbers between these two fundamental systems.

What is the Decimal System (Base-10)?

The decimal system is the number system we use every day. It uses ten unique digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) and is a positional system, meaning the position of a digit determines its value. Each position represents a power of 10. For example, the number 123 can be broken down as:

• 1 × 10² (100)
• 2 × 10¹ (10)
• 3 × 10⁰ (1)

Summing these gives 100 + 20 + 3 = 123.

What is the Binary System (Base-2)?

The binary system uses only two digits: 0 and 1. It's also a positional system, but each position represents a power of 2. This system is crucial for computers because electronic circuits can easily represent these two states (on/off, high/low voltage). A single binary digit is called a "bit."

For example, the binary number 1011 can be understood as:

• 1 × 2³ (8)
• 0 × 2² (4)
• 1 × 2¹ (2)
• 1 × 2⁰ (1)

Summing these gives 8 + 0 + 2 + 1 = 11. So, binary 1011 is equivalent to decimal 11.

How to Convert Binary to Decimal

To convert a binary number to its decimal equivalent, you multiply each digit by the corresponding power of 2 and then sum the results. Start from the rightmost digit (least significant bit) with 2⁰, then 2¹, 2², and so on.

Example: Convert binary 11010 to decimal.

• 0 × 2⁰ = 0 × 1 = 0
• 1 × 2¹ = 1 × 2 = 2
• 0 × 2² = 0 × 4 = 0
• 1 × 2³ = 1 × 8 = 8
• 1 × 2⁴ = 1 × 16 = 16

Sum: 0 + 2 + 0 + 8 + 16 = 26. So, 11010₂ = 26₁₀.

How to Convert Decimal to Binary

To convert a decimal number to its binary equivalent, you use the method of repeated division by 2. You divide the decimal number by 2, note the remainder, and then divide the quotient by 2 again. You continue this process until the quotient is 0. The binary number is formed by reading the remainders from bottom to top.

Example: Convert decimal 26 to binary.

• 26 ÷ 2 = 13 remainder 0
• 13 ÷ 2 = 6 remainder 1
• 6 ÷ 2 = 3 remainder 0
• 3 ÷ 2 = 1 remainder 1
• 1 ÷ 2 = 0 remainder 1

Reading the remainders from bottom to top gives 11010. So, 26₁₀ = 11010₂.

This converter simplifies these processes, making it easy to switch between the human-readable decimal system and the computer-friendly binary system.