Converting decimal numbers to binary is a fundamental operation in computer science, as binary is the base of the number system used by computers.
In this tutorial, we will discuss how to write a JavaScript program to convert decimal numbers to binary using a simple algorithm.
The algorithm we will use is based on the fact that any decimal number can be expressed as a sum of powers of 2.
For example, the number 13 can be expressed as:
12^3 + 12^2 + 02^1 + 12^0 = 1101 (binary)
To convert a decimal number to binary, we start by dividing the number by 2 and recording the remainder.
We then divide the quotient by 2 and record the remainder again, repeating this process until the quotient becomes 0.
The binary number is then obtained by writing down the remainders in reverse order.
Let’s now write a JavaScript function that implements this algorithm:
function decimalToBinary(decimal) {
let binary = "";
while (decimal > 0) {
binary = (decimal %% 2) + binary;
decimal = Math.floor(decimal / 2);
}
return binary;
}
The function takes a decimal number as input and returns its binary representation as a string.
We start by initializing an empty string to store the binary digits. We then enter a while loop that continues as long as the decimal number is greater than 0.
Inside the loop, we compute the remainder of the decimal number when divided by 2 and append it to the beginning of the binary string.
We then update the decimal number by dividing it by 2 and discarding any remainder.
We repeat this process until the decimal number becomes 0. Finally, we return the binary string.
Let’s test our function with a few examples:
console.log(decimalToBinary(13)); // Output: "1101" console.log(decimalToBinary(42)); // Output: "101010" console.log(decimalToBinary(255)); // Output: "11111111"
As we can see, the function correctly converts decimal numbers to binary. We can use this function in any JavaScript program that requires binary arithmetic, such as bitwise operations or encoding/decoding data in binary formats.
In conclusion, converting decimal numbers to binary is a fundamental operation in computer science, and we have demonstrated how to write a simple JavaScript program to accomplish this task.
