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Python code to convert SOP to POS
  • Last Updated : 19 Nov, 2020

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).

Examples:

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')

Approach:

  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                 
            Min_terms.append(b) 
  
            # empty the string         
            a =""                         
            i+= 1
        else
  
            # checking whether variable is complemented or not 
            if(i + 1 != len(SOP) and SOP[i + 1]=="'"): 
  
                # concatenating the string with '0' 
                a+='0' 
  
                # incrementing by 2 because 1 for alphabet and 
                # another for "'"                        
                i+= 2                            
            else
  
                # concatenating the string with '1' 
                a+='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'+
  
            # appending the max terms(integer) in the list 
            Max_terms.append(b)     
  
    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     
            else
  
                # 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__"
    main() 
Output:
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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