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Converting Binary to Decimal in python (without built in binary function)

Alrighty, first post here, so please forgive and ignore if the question is not workable;

Background: I'm in computer science 160. I haven't taken any computer related classes since high school, so joining this class was a big shift for me. It all seemed very advanced. We have been working in Python and each week we are prompted to write a program.

I have been working with this problem for over a week and am having a hard time even starting.
The prompt is to read an integer containing only 1's and 0's, process the binary number digit by digit and report the decimal equivalent. Now, I have gotten some tips from a classmate and it sent me at least in a direction.

Set up a couple of counters; using the % operator to check the remainder of the number divided by 2, and slicing off the last number (to the right) to move on to and process the next digit.

I am having an incredibly hard time wrapping my head around what formula to use on the binary digits themselves which will convert the number to decimal.

setbitval = 0
counter = 0
user = int(input("enter a binary value. "))
if user % 2 == 1:
 user = (user/10) - .1
 setbitval += 1

This is all I've got so far.. My thinking is getting in the way. I've searched and searched, even through these forums.

Any information or thoughts are extremely appreciated,
T

Edit: okay guys, everyone's help has been extremely useful but I'm having a problem checking if the user input is not a binary number.

for i in reversed(bits): 
decimal += 2**counter * int(i)
counter += 1

This is the formula someone here gave me and I've been trying different iterations of "for i in bits: if i in bits: != 0 or 1" and also "if i in bits:>= 1 or <=0".
Any thoughts?

Answer*

I’d recommend reading the following articles on Wikipedia:
https://en.wikipedia.org/wiki/Radix
https://en.wikipedia.org/wiki/Binary_number

The first one gives you an idea how the numeral systems work in general and the second one explains and shows the formula to convert between binary and decimal systems.
Try to implement the solution after reading this. That’s what I did when I dealt with this problem. If that doesn’t help, let me know and I’ll post the code.

Hopefully, this code clarifies things a bit.

 x = input("Enter binary number: ").strip()
 decimal = 0
 for i in range(len(x)):
 decimal += int(x[i]) * 2**abs((i - (len(x) - 1)))
 print(decimal)

This code takes in a binary number as a string, converts it to a decimal number and outputs it as an integer. The procedure is the following:

1st element of binary number * 2^(length of binary number - 1)

2nd element of binary number * 2^(length of binary number - 2)

and so on till we get to the last element and ...2^0

If we take number 10011, the conversion using this formula will look like this:
1*2^4 + 0*2^3 + 0*2^2 + 1*2^1 + 1*2^0, which equals to 19.

This code, however, assumes that the binary number is valid. Let me know if it helps.

Another implementation using while loop might look like this. Maybe it'll be easier to understand than the code with the for loop.

 x = input("Enter binary number: ").strip()
 decimal = 0
 index = 0
 exp = len(x) - 1
 while index != len(x):
 decimal += int(x[index]) * 2**exp
 index += 1
 exp -= 1
 print(decimal)

In this one we start from the beginning of the number with the highest power, which is *length of binary number minus one*, we loop through the number, lowering the power and changing index.

Regarding checking if number is binary.
Try using helper function to determine if number is binary and then insert this function inside your main function. For example:

 def is_binary(x):
 """ Returns True if number x is binary and False otherwise.
 
 input: x as a string
 """
 for i in list(x):
 if i not in ["1", "0"]:
 return False
 return True
 
 
 def binary_decimal(x):
 """ Converts binary to decimal.
 input: binary number x as a string
 output: decimal number as int
 """
 if not is_binary(x):
 return "Number is invalid"
 decimal = 0
 for i in range(len(x)):
 decimal += int(x[i]) * 2**abs((i - (len(x) - 1)))
 return decimal

The first function checks if number consists only of ones and zeros and the second function actually converts your number only if it's binary according to the first function.
You can also try using assert statement or try / except if you'd better raise an error if number is not binary instead of simply printing the message.

Of course, you can implement this solution without any functions.

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Thanks for the comment and link. If you were to post code, it may be clear by now that it probably wouldn't do me much good other than copy and pasting. Thank you again, and I will read into the wiki page.

relytkadReh
– relytkadReh

2017年11月15日 23:54:08 +00:00
Commented Nov 15, 2017 at 23:54
So I did run into the formula for converting to decimal which i had found before. The other day I got lost in trying to use the "len()" of the user input and emulating the formula for conversion. It was overwhelming.

relytkadReh
– relytkadReh

2017年11月16日 00:18:21 +00:00
Commented Nov 16, 2017 at 0:18
I’m having trouble checking whether or not the user input is binary or not. Is there a way to implement that before the formula?

relytkadReh
– relytkadReh

2017年11月19日 01:08:31 +00:00
Commented Nov 19, 2017 at 1:08
I've added some code with description. Let me know if it helps.

Vlad
– Vlad

2017年11月19日 08:35:15 +00:00
Commented Nov 19, 2017 at 8:35

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Converting Binary to Decimal in python (without built in binary function)

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