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Binary to HexaDecimal
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The program is written here to convert a binary number into its equivalent hexadecimal number.
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.
Now this decimal value will be converted to its equivalent hexadecimal by dividing the number with 16, again divide the quotient with 16 and so on until the number becomes 0. The remainder after each division will be shown in the reversed order. Hence, we will get the hexadecimal number. The example is given below:
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Therefore, the equivalent hexadecimal number is
Algorithm
INPUT: A binary number
OUTPUT: Equivalent Hexadecimal Number
PROCESS:
Step 1: [Taking the input]
Read n [the binary number]
Step 2: [Converting from binary to hexadecimal]
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]
[Converting from decimal to hexadecimal]
While d>0 repeat
Set r<- d mod 16
If r≤9 then
Concatenate the value of variable ‘r’ with ‘s’ in reversed order.
Else if r=10 then
Concatenate ‘A’ with ‘s’ in reversed order.
Else if r=11 then
Concatenate ‘B’ with ‘s’ in reversed order.
Else if r=12 then
Concatenate ‘C’ with ‘s’ in reversed order.
Else if r=13 then
Concatenate ‘D’ with ‘s’ in reversed order.
Else if r=14 then
Concatenate ‘E’ with ‘s’ in reversed order.
Else if r=15 then
Concatenate ‘F’ with ‘s’ in reversed order.
Set d<-d/16
[End of ‘while’ loop]
[Printing the hexadecimal number]
Print "The hexadecimal number is: s”
Step 3: Stop.
Code
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;
}
//converting from decimal to hexadecimal
p=0;
while(d>0)-----------------------------------------------O(m)
{
r=d%16;
if(r<=9)
hex[p++]=(char)(r+48);
else if(r==10)
hex[p++]='A';
else if(r==11)
hex[p++]='B';
else if(r==12)
hex[p++]='C';
else if(r==13)
hex[p++]='D';
else if(r==14)
hex[p++]='E';
else if(r==15)
hex[p++]='F';
d=d/16;
}
The time complexity of this program is O(k+m) where ‘k’ is the number of digits of the binary number and ‘m’ is the number of digits of the decimal number.
SPACE COMPLEXITY:
The space complexity of this program is O(1) as it requires a constant number of memory spaces to execute the program.
