Understanding how to convert between binary and decimal numbers is fundamental in computer science and programming.

In this article, I’ll show you the Python functions that enable you to seamlessly convert binary numbers to their decimal counterparts and vice versa.

Convert Binary String to Decimal Number

Below is my code which performs the conversion:

def binary_to_decimal(binary_str):
    decimal = 0
    power = len(binary_str) - 1
    
    for digit in binary_str:
        if digit == '1':
            decimal += 2 ** power
        power -= 1
    
    return decimal

# Example showing how to use the above function
binary_num = "1010"
decimal_num = binary_to_decimal(binary_num)
print("Decimal equivalent of", binary_num, "is", decimal_num)

Output:

Decimal equivalent of 1010 is 10

Let me explain the conversion steps to you.

• Start by setting decimal to 0, which will store the decimal equivalent, and power to the length of the binary number minus 1. power is used to calculate the position value of each binary digit.
• Loop through each digit in the binary number from left to right.
• For each binary digit, if it’s ‘1’, add 2 raised to the power of its position value (power) to the decimal variable.
• After processing each digit, decrement the power variable by 1 to move to the next lower position value.
• Once all digits are processed, return the decimal variable, which now holds the decimal equivalent of the binary number.

These are simple steps, you can accurately convert any binary number to its decimal representation using the provided Python code.

Convert Decimal Number to Binary

Below is my code which performs the reverse conversion:

def decimal_to_binary(decimal_num):
    binary = ""
    
    while decimal_num > 0:
        remainder = decimal_num % 2
        binary = str(remainder) + binary
        decimal_num //= 2
    
    return binary if binary else "0"

# Example showing how to use the above function
decimal_num = 10
binary_num = decimal_to_binary(decimal_num)
print("Binary equivalent of", decimal_num, "is", binary_num)

Output:

Binary equivalent of 10 is 1010

Let’s explain the steps involved in converting a decimal to binary:

• Begin by setting an empty string binary which will store the binary equivalent of the decimal number.
• Start a loop where you repeatedly divide the decimal number by 2 until it becomes 0. This process is often referred to as “integer division”.
• For each division, calculate the remainder (remainder) by taking the modulo 2 of the current decimal number.
• Add the remainder to the left side of the binary string. This is done because we’re building the binary number from right to left.
• Update the decimal number by performing integer division by 2, effectively shifting it to the right by one position.
• Continue this process until the decimal number becomes 0.
• Once the decimal number becomes 0, return the binary string, which now holds the binary equivalent of the original decimal number.

With these above 2 examples, you can accurately convert any decimal number to its binary representation and vice versa. You can contact me for any doubts or clarifications.