Python program to convert POS to SOP

Write a program in Python to convert standard POS(product of sums) form to standard SOP(sum of products) form.

Assumptions: The input POS expression is standard. The variables in POS expression are continuous i.e. if expression contains variable A then it will have variables B, C respectively and each Sum term contains the alphabets in sorted order i.e. A + B + C (not like B+A+C).

Examples:

 Input : (A + B + C).(A + B + C').(A + B' + C).(A' + B + C)
Output : A'BC + AB'C + ABC' + ABC

Input : (A + B).(A' + B')
Output : A'B + AB'

Approach:

1. First of all convert each sum term to its equivalent binary form. For example, if (A+B+C’) then take 0 for uncomplement variable(A, B) and take 1 for complement variable(C) so binary conversion is 011) and then finally equivalent to its decimal form(for ex: 001 = 1) and store in a list.
2. Now for SOP form take all those terms which are not present in the list formed in step 1st and then convert each term to binary and hence change to POS form. For example –
   Suppose 4 was not in the list then 5==> 101 (binary)
   Now, replace 0 by complement variables(B)
   replace 1 by uncomplement variables(A, C)
   101 ==> AB’C
   After each individual sum term use ‘+’
   ex: AB’C+AB’C’

Below is the Python implementation of above approach:

# Python code to convert standard POS form
# to standard SOP form

# Function to calculate no. of variables
# used in POS expression
def count_no_alphabets(POS):
    i = 0
    no_var = 0

    # As expression is standard so total no.
    # of alphabets will be equal
    # to alphabets before first '.' character
    while (POS[i]!='.'):

        # checking if character is alphabet
        if (POS[i].isalpha()):
            no_var+= 1
        i+= 1
    return no_var

# Function to calculate the max terms in integers
def Cal_Max_terms(Max_terms, POS):
    a = ""
    i = 0
    while (i<len(POS)):
        if (POS[i]=='.'):

            # converting binary to decimal
            b = int(a, 2)

            # insertion of each min term(integer) into the list
            Max_terms.append(b)

            # empty the string
            a =""
            i+= 1

        elif(POS[i].isalpha()):

            # checking whether variable is complemented or not
            if(i + 1 != len(POS) and POS[i + 1]=="'"):

                # concatenating the string with '0'
                a += '1'

                # incrementing by 2 because 1 for alphabet and
                # another for "'"
                i += 2
            else:

                # concatenating the string with '1'
                a += '0'
                i += 1
        else:
            i+= 1

    # insertion of last min term(integer) into the list
    Max_terms.append(int(a, 2))

# Function to calculate the min terms in binary then
# calculate SOP form of POS
def Cal_Min_terms(Max_terms, no_var, start_alphabet):

    # declaration of the list
    Min_terms =[]

    # calculation of total no. of terms that can be
    # formed by no_var variables
    max = 2**no_var
    for i in range(0, max):

        # checking whether the term is not
        # present in the max terms
        if (Max_terms.count(i)== 0):

            # converting integer to binary and then
            # taking the value from 2nd index as 1st
            # two index contains '0b'
            b = bin(i)[2:]

            # loop used for inserting 0's before the
            # binary value so that its length will be
            # equal to no. of variables present in
            # each product term
            while(len(b)!= no_var):
                b ='0'+b

            # appending the max terms(integer) in the list
            Min_terms.append(b)

    SOP = ""

    # loop till there are min terms
    for i in Min_terms:

        # acquire the starting variable came from
        # main function in every product term
        value = start_alphabet

        # loop till there are 0's or 1's in each min term
        for j in i:

            # checking for complement variable to be used
            if (j =='0'):

                # concatenating value, ' and + in string POS
                SOP = SOP + value+"'"

            # checking for uncomplement variable to be used
            else:

                # concatenating value and + in string POS
                SOP = SOP + value

            # increment the alphabet by 1
            value = chr(ord(value)+1)

        # appending the SOP string by '+" after
        # every product term
        SOP = SOP+ "+"

    # for discarding the extra '+' in the last
    SOP = SOP[:-1]
    return SOP

# main function
def main():

    # input1
    POS_expr ="(A+B+C).(A+B+C').(A+B'+C).(A'+B + C)"
    Max_terms = []

    no_var = count_no_alphabets(POS_expr)
    Cal_Max_terms(Max_terms, POS_expr)
    SOP_expr = Cal_Min_terms(Max_terms, no_var, POS_expr[1])

    print("Standard SOP form of " + POS_expr + " ==> " + SOP_expr)

    # input2
    POS_expr ="(A + B).(A'+B')"
    Max_terms = []

    no_var = count_no_alphabets(POS_expr)
    Cal_Max_terms(Max_terms, POS_expr)
    SOP_expr = Cal_Min_terms(Max_terms, no_var, POS_expr[1])

    print ("Standard SOP form of " + POS_expr + " ==> " + SOP_expr)

# Driver code
if __name__=="__main__":
    main()

Output:

Standard SOP form of (A+B+C).(A+B+C').(A+B'+C).(A'+B + C)  ==>  A'BC+AB'C+ABC'+ABC
Standard SOP form of (A + B).(A'+B')  ==>  A'B+AB'