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).


 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'


  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                 
            # empty the string         
            a =""                         
            i+= 1
            # 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                            
                # concatenating the string with '1' 
                a += '0'                        
                i += 1
            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'+
            # appending the max terms(integer) in the list 
    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     
                # 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__"



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'

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