# CREATE OWN LIBRARY

## Binary to Decimal

Back to Programming

### Description

The binary number is taken as input from the user. The decimal number can be calculated by adding the products of each digit and the power of 2 starting from 0 from the right to left.

For example, the binary number is 101101.

The decimal number will be:

= 32 + 0 + 8 + 4 + 0 + 1 = 45.

The value 45 will be printed.

### Algorithm

INPUT: The binary number.

OUTPUT: The decimal number.

PROCESS:

Step 1: [Taking the input]

Step 2: [Converting from binary to decimal]

Set d<-0

Set p<-0

[Converting from binary to decimal]

While n>0 repeat

[Calculating the power of 2 and multiplied with the binary digit]

Set d<-d+(n mod 10)×2p

[Increasing the power]

Set p<-p+1

Set n<-n/10

[End of ‘while’ loop]

[Printing the decimal number]

Print "The decimal number is d”

Step 3: Stop.

## TIME COMPLEXITY:

while(n>0)-------------------------------------O(k)

{

//calculating the power of 2 and multiplied

//with the binary digit

d=d+(n%10)*pow(2,p);

//increasing the power

p+=1;

n=n/10;

}

The time complexity can be given as O(k) where ‘k’ is the number of digits of the binary numbers. The complexity can also be defined as O(log n) if n is the equivalent decimal number.

## SPACE COMPLEXITY:

The space complexity is O(1) as the program requires a constant number of memory spaces to execute the program for any given input.