Python code to convert SOP to POS

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

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


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

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


  1. First of all convert each product term to its equivalent binary form(for ex: if ABC’ then take 1 for uncomplement variable(A, B) and take 0 for complement variable(C) so binary conversion is 110) and then finally equivalent to its decimal form(for ex: 110 = 6) and store in a list.
  2. Now for POS 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 SOP form.For ex: suppose 5 was not in the list then
    5 ==> 101 (binary)
    Now, replace 1 by complement variables(A, C)
    replace 0 by uncomplement variables(B)
    and between the variables use ‘+’
    101 ==> A’+B+C’
    After each individual sum term use ‘.’
    For more clarity use brackets between each individual term.
    ex: (A’+B+C’).(A+B+C’)

Python Code





# Python code to convert standard SOP form 
# to standard POS form
# function to calculate no. of variables 
# used in SOP expression
def count_no_alphabets(SOP):
    i = 0
    no_var = 0
    # As expression is standard so total no.
    # of alphabets will be equal 
    # to alphabets before first '+' character
    while (SOP[i]!='+'): 
        # checking if character is alphabet            
        if (SOP[i].isalpha()):       
            no_var+= 1
        i+= 1
    return no_var
# function to calculate the min terms in integers
def Cal_Min_terms(Min_terms, SOP):
    a =""
    i = 0
    while (i<len(SOP)):
        if (SOP[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(SOP) and SOP[i + 1]=="'"): 
                # concatenating the string with '0'
                # incrementing by 2 because 1 for alphabet and 
                # another for "'"                          
                i+= 2                             
                # concatenating the string with '1'
                i+= 1
    # insertion of last min term(integer) into the list      
    Min_terms.append(int(a, 2))            
# function to calculate the max terms in binary then 
# calculate POS form of SOP   
def Cal_Max_terms(Min_terms, no_var, start_alphabet): 
    # declaration of the list
    Max_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 min terms
        if (Min_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
    POS ="" 
    # loop till there are max terms                          
    for i in Max_terms:  
        # before every sum term append POS by '('           
        POS = POS+"("   
        # acquire the starting variable came from  
        # main function in every sum term              
        value = start_alphabet  
        # loop till there are 0's or 1's in each max term      
        for j in i:
            # checking for complement variable to be used                 
            if (j =='1'):
                # concatenating value, ' and + in string POS                   
                POS = POS + value+"'+"  
            # checking for uncomplement variable to be used     
                # concatenating value and + in string POS                       
                POS = POS + value+"+" 
            # increment the alphabet by 1       
            value = chr(ord(value)+1)
        # for discarding the extra '+' in the last      
        POS = POS[:-1]  
        # appending the POS string by ')." after
        # every sum term                   
        POS = POS+")." 
    # for discarding the extra '.' in the last                    
    POS = POS[:-1]                         
    return POS
# main function   
def main():
    # input1
    SOP_expr ="ABC'+A'BC + ABC + AB'C"
    Min_terms =[]
    no_var = count_no_alphabets(SOP_expr)
    Cal_Min_terms(Min_terms, SOP_expr)
    POS_expr = Cal_Max_terms(Min_terms, no_var, SOP_expr[0])
    print "Standard POS form of", SOP_expr, " ==> ", POS_expr
    # input2
    SOP_expr ="A'B + AB'"
    Min_terms =[]
    no_var = count_no_alphabets(SOP_expr)
    Cal_Min_terms(Min_terms, SOP_expr)
    POS_expr = Cal_Max_terms(Min_terms, no_var, SOP_expr[0])
    print "Standard POS form of", SOP_expr, " ==> ", POS_expr
    # input3
    SOP_expr ="xyz'+x'y'z'+xy'z"
    Min_terms =[]
    no_var = count_no_alphabets(SOP_expr)
    Cal_Min_terms(Min_terms, SOP_expr)
    POS_expr = Cal_Max_terms(Min_terms, no_var, SOP_expr[0])
    print "Standard POS form of", SOP_expr, " ==> ", POS_expr
# driver code    
if __name__=="__main__":



Standard POS form of ABC'+A'BC + ABC + AB'C  ==>  (A+B+C).(A+B+C').(A+B'+C).(A+B'+C').(A'+B+C).(A'+B+C')
Standard POS form of A'B + AB'  ==>  (A+B).(A+B').(A'+B)
Standard POS form of xyz'+x'y'z'+xy'z  ==>  (x+y+z').(x+y'+z).(x+y'+z').(x'+y+z).(x'+y'+z')

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