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:
- 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.
- 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'
