Python program to print number of bits to store an integer and also the number in Binary format

Given an integer, the task is to write a Python program to print the number of bits to store that integer and also print the same number in Binary format.

Example:

Input: n = 10

Output: 

Number of bits to store the number: 4        

Binary value: 0b1010

Input: n = 120

Output:

Number of bits to store the number: 7

Binary value: 0b1111000

The Task can be done in 3 ways and all of them are given below:

Method 1: Using loops

In this, we will use the most basic method of converting the given number into binary form by dividing it by 2 until the number becomes zero and storing the remainder after each division. Continuing in this fashion, the size of the array will give the number of bits to store an integer and the reverse of the array with give the Binary format of the integer.

Approach

• Declare or take input
• Keep dividing it by 2 and store remainder obtained
• At the end of the process print its binary equivalent as well as the number of bits required to store it.

Example :

Python3

list1 = []
num = 10

while (num > 0):
    list1.append(num % 2)
    num = num//2

print("Number of bits required to store 10:", len(list1))
print("Binary Representatiaon:", end="")
for i in reversed(list1):
    print(list1[i], end="")

Output:

Number of bits required to store 10: 4

Binary Representatiaon:1010

Method 2:Using Recursion

This code perform same task as given in method 1, but instead of using loops we will use recursion.

Approach:

• Declare or take input
• Keep dividing it by 2 and store remainder obtained using a recursive function
• At the end of the process print its binary equivalent as well as the number of bits required to store it.

Example:

Python3

def decimalToBinary(n, x):

    if n > 1:
        # divide with integral result
        # (discard remainder)
        x = decimalToBinary(n//2, x)

    print(n % 2, end="")
    return x+1


# Driver code
if __name__ == '__main__':
    x = 0
    print("Binary Representation of 17:", end=" ")

    x = decimalToBinary(17, x)

    print()
    print("Number of bits required to store 17:", end=" ")
    print(x)

Output:

Binary Representation of 17: 10001

Number of bits required to store 17: 5

Method 3: Using in-built function

Python comes with built-in sophisticated functions to perform the same tasks in just few lines. To find the total number of bits to store an integer, we use bit_length() function, it is called with the number (an integer value) and returns the total number of bits to store the given number.

Syntax: int.bit_length(n)

Parameter: n, where it is an integer 

Returns: The number of bits required to represent an integer in binary, excluding the sign and leading zeros.

To print binary value of a given integer, we use bin() function it accepts the number as an argument and returns the binary value.

Syntax : bin(a)

Parameters :

a : an integer to convert

Return Value :
A binary string of an integer or int object.

Exceptions :
Raises TypeError when a float value is sent in arguments.

The output produced will have 0b in front of a number, it is just an indicator that what follows it is a binary representation. You can remove it if you want.

Example:

Python3

num = 120

s = bin(120)

print("Number of bits required to store 120:", end=" ")
print(num.bit_length())

print("Binary Representation", end=" ")
print(s)

Output

Number of bits required to store 120: 7
Binary Representation 0b1111000

Output:

Number of bits required to store 120: 7

Binary Representation 0b1111000

 Using the math module:

Approach:

Import the math module.
Define the print_bits_and_binary() function that takes an integer n as input.
Calculate the number of bits required to store the integer using the int() function and the math.log2() function. Add 1 to this value to include the sign bit if the integer is negative.
Convert the integer to binary using the bin() function.
Print the number of bits required to store the integer and its binary value.

Python3

import math

def print_bits_and_binary(n):
    bits = int(math.log2(n))+1
    binary = bin(n)
    print("Number of bits to store the number:", bits)
    print("Binary value:", binary)

n = 10
print_bits_and_binary(n)

n = 120
print_bits_and_binary(n)

Output

Number of bits to store the number: 4
Binary value: 0b1010
Number of bits to store the number: 7
Binary value: 0b1111000

Time complexity: O(1) for both cases, as the math.log2() and bin() functions have constant time complexity.
Auxiliary Space: O(1), as only a few variables are created.