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:
- 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.
- 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'+b # 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')
