3 Ways to Convert from Decimal to Binary
In the world of computing, understanding number systems is essential. One such widely utilized number system is binary, which comprises only two digits – 0 and 1. Converting decimal numbers to binary is a fundamental skill, whether you’re a computer scientist, engineer, or coding enthusiast.
Here are three different methods to convert decimal numbers to their binary equivalents:
1. Division by 2 method:
The division by 2 method entails dividing the given decimal number by 2 repeatedly until the quotient is zero. The sequence of remainders will represent the binary equivalent in reverse order.
Steps:
– Divide the given decimal number by 2.
– Record the remainder.
– Divide the quotient obtained in step 1 by 2 again.
– Repeat this process until the quotient becomes zero.
– Write down the remainders in reverse order as your answer.
Example: Convert 27 to binary
27 / 2 = 13 (remainder = 1)
13 / 2 = 6 (remainder = 1)
6 / 2 = 3 (remainder = 0)
3 / 2 = 1 (remainder = 1)
1 / 2 = 0 (remainder = 1)
The binary representation of decimal number “27” is “11011”.
2. Subtraction and Doubling method:
The subtraction and doubling method involves finding the highest power of two that subtracts from your decimal number without resulting in a negative result. Subtract this value from your decimal number and proceed similarly with the remainder.
Steps:
– Find the largest power of two (say, N) that can be subtracted from your decimal number without giving a negative result.
– Write “1” at position N in your binary answer. Write “0” at all positions less than N.
– Subtract N from your decimal number.
– Repeat steps one through three with the remainder, adding the result to the existing binary number.
– When the remainder is zero or one, write down that final remainder as the last digit in your binary answer.
Example: Convert 45 to binary
2^5 = 32 < 45, so write “1” at position 5: (1[0000])
45 – 32 = 13
2^3 = 8 < 13, so write “1” at position 3: (10100)
13 – 8 = 5
2^2 = 4 < 5, so write “1” at position 2: (10110)
5 – 4 = 1
Write “1” at position 0: (101101)
The binary representation of decimal number “45” is “101101”.
3. Using a programming language:
Most modern programming languages have built-in functions for converting decimal numbers to binary. Here’s an example using Python:
“`python
def decimal_to_binary(decimal_number):
return bin(decimal_number)[2:]
decimal_number = int(input(“Enter a decimal number: “))
binary_number = decimal_to_binary(decimal_number)
print(“The binary representation of”, decimal_number, “is:”, binary_number)
“`
The program calculates the respective binary value with just a few lines of code.
These three methods will help you comfortably convert decimal numbers to binary. Whether you’re taking on large-scale computing tasks, learning programming languages, or simply looking to understand the basics of number systems, the ability to convert between bases is invaluable.