Binary Number Calculator

Binary Number Converter

Binary to Decimal Conversion

Decimal to Binary Conversion

function convertBinaryToDecimal() { var binaryString = document.getElementById("binaryInput").value.trim(); var resultDiv = document.getElementById("binaryToDecimalResult"); resultDiv.style.display = "none"; resultDiv.style.backgroundColor = "#d4edda"; resultDiv.style.color = "#155724"; if (binaryString === "") { resultDiv.innerHTML = "Please enter a binary number."; resultDiv.style.display = "block"; resultDiv.style.backgroundColor = "#f8d7da"; resultDiv.style.color = "#721c24"; return; } if (!/^[01]+$/.test(binaryString)) { resultDiv.innerHTML = "Invalid binary number. Please use only 0s and 1s."; resultDiv.style.display = "block"; resultDiv.style.backgroundColor = "#f8d7da"; resultDiv.style.color = "#721c24"; return; } try { var decimalValue = parseInt(binaryString, 2); resultDiv.innerHTML = "Decimal Equivalent: " + decimalValue; resultDiv.style.display = "block"; } catch (e) { resultDiv.innerHTML = "An error occurred during conversion. Please check your input."; resultDiv.style.display = "block"; resultDiv.style.backgroundColor = "#f8d7da"; resultDiv.style.color = "#721c24"; } } function convertDecimalToBinary() { var decimalString = document.getElementById("decimalInput").value.trim(); var resultDiv = document.getElementById("decimalToBinaryResult"); resultDiv.style.display = "none"; resultDiv.style.backgroundColor = "#d1ecf1"; resultDiv.style.color = "#0c5460"; if (decimalString === "") { resultDiv.innerHTML = "Please enter a decimal number."; resultDiv.style.display = "block"; resultDiv.style.backgroundColor = "#f8d7da"; resultDiv.style.color = "#721c24"; return; } var decimalValue = Number(decimalString); if (isNaN(decimalValue) || !Number.isInteger(decimalValue) || decimalValue < 0) { resultDiv.innerHTML = "Invalid decimal number. Please enter a non-negative integer."; resultDiv.style.display = "block"; resultDiv.style.backgroundColor = "#f8d7da"; resultDiv.style.color = "#721c24"; return; } try { var binaryValue = decimalValue.toString(2); resultDiv.innerHTML = "Binary Equivalent: " + binaryValue; resultDiv.style.display = "block"; } catch (e) { resultDiv.innerHTML = "An error occurred during conversion. Please check your input."; resultDiv.style.display = "block"; resultDiv.style.backgroundColor = "#f8d7da"; resultDiv.style.color = "#721c24"; } }

Understanding Binary Numbers and Conversions

Binary numbers are the fundamental language of computers. Unlike the decimal system (base-10) that we use daily, which employs ten unique digits (0-9), the binary system (base-2) uses only two digits: 0 and 1. Each position in a binary number represents a power of 2, just as each position in a decimal number represents a power of 10.

Why Binary?

Computers operate using electrical signals that are either 'on' or 'off'. These two states are perfectly represented by the binary digits 1 and 0, making binary the most efficient way for digital systems to process and store information. From simple calculations to complex software, everything a computer does is ultimately broken down into binary code.

How to Convert Binary to Decimal

Converting a binary number to its decimal equivalent involves understanding positional notation. Each digit in a binary number is multiplied by a power of 2, corresponding to its position, starting from 2⁰ for the rightmost digit. The results are then summed up.

Example: Convert 101101₂ to Decimal

• Starting from the rightmost digit:
• 1 × 2⁰ = 1 × 1 = 1
• 0 × 2¹ = 0 × 2 = 0
• 1 × 2² = 1 × 4 = 4
• 1 × 2³ = 1 × 8 = 8
• 0 × 2⁴ = 0 × 16 = 0
• 1 × 2⁵ = 1 × 32 = 32

Summing these values: 32 + 0 + 8 + 4 + 0 + 1 = 45₁₀. So, 101101₂ is 45 in decimal.

How to Convert Decimal to Binary

Converting a decimal number to binary typically uses the method of repeated division by 2. You divide the decimal number by 2, record the remainder, and then divide the quotient by 2 again. You continue this process until the quotient becomes 0. The binary number is then formed by reading the remainders from bottom to top.

Example: Convert 45₁₀ to Binary

• 45 ÷ 2 = 22 remainder 1
• 22 ÷ 2 = 11 remainder 0
• 11 ÷ 2 = 5 remainder 1
• 5 ÷ 2 = 2 remainder 1
• 2 ÷ 2 = 1 remainder 0
• 1 ÷ 2 = 0 remainder 1

Reading the remainders from bottom to top gives us 101101₂. So, 45₁₀ is 101101 in binary.

This calculator simplifies these conversions, allowing you to quickly switch between the binary and decimal representations of numbers, which is invaluable for students, programmers, and anyone working with digital systems.