from __future__ import annotations def compare_string(string1: str, string2: str) -> str: """ >>> compare_string('0010','0110') '0_10' >>> compare_string('0110','1101') 'X' """ l1 = list(string1) l2 = list(string2) count = 0 for i in range(len(l1)): if l1[i] != l2[i]: count += 1 l1[i] = "_" if count > 1: return "X" else: return "".join(l1) def check(binary: list[str]) -> list[str]: """ >>> check(['0.00.01.5']) ['0.00.01.5'] """ pi = [] while 1: check1 = ["$"] * len(binary) temp = [] for i in range(len(binary)): for j in range(i + 1, len(binary)): k = compare_string(binary[i], binary[j]) if k != "X": check1[i] = "*" check1[j] = "*" temp.append(k) for i in range(len(binary)): if check1[i] == "$": pi.append(binary[i]) if len(temp) == 0: return pi binary = list(set(temp)) def decimal_to_binary(no_of_variable: int, minterms: list[float]) -> list[str]: """ >>> decimal_to_binary(3,[1.5]) ['0.00.01.5'] """ temp = [] s = "" for m in minterms: for i in range(no_of_variable): s = str(m % 2) + s m //= 2 temp.append(s) s = "" return temp def is_for_table(string1: str, string2: str, count: int) -> bool: """ >>> is_for_table('__1','011',2) True >>> is_for_table('01_','001',1) False """ l1 = list(string1) l2 = list(string2) count_n = 0 for i in range(len(l1)): if l1[i] != l2[i]: count_n += 1 if count_n == count: return True else: return False def selection(chart: list[list[int]], prime_implicants: list[str]) -> list[str]: """ >>> selection([[1]],['0.00.01.5']) ['0.00.01.5'] >>> selection([[1]],['0.00.01.5']) ['0.00.01.5'] """ temp = [] select = [0] * len(chart) for i in range(len(chart[0])): count = 0 rem = -1 for j in range(len(chart)): if chart[j][i] == 1: count += 1 rem = j if count == 1: select[rem] = 1 for i in range(len(select)): if select[i] == 1: for j in range(len(chart[0])): if chart[i][j] == 1: for k in range(len(chart)): chart[k][j] = 0 temp.append(prime_implicants[i]) while 1: max_n = 0 rem = -1 count_n = 0 for i in range(len(chart)): count_n = chart[i].count(1) if count_n > max_n: max_n = count_n rem = i if max_n == 0: return temp temp.append(prime_implicants[rem]) for i in range(len(chart[0])): if chart[rem][i] == 1: for j in range(len(chart)): chart[j][i] = 0 def prime_implicant_chart( prime_implicants: list[str], binary: list[str] ) -> list[list[int]]: """ >>> prime_implicant_chart(['0.00.01.5'],['0.00.01.5']) [[1]] """ chart = [[0 for x in range(len(binary))] for x in range(len(prime_implicants))] for i in range(len(prime_implicants)): count = prime_implicants[i].count("_") for j in range(len(binary)): if is_for_table(prime_implicants[i], binary[j], count): chart[i][j] = 1 return chart def main() -> None: no_of_variable = int(input("Enter the no. of variables\n")) minterms = [ float(x) for x in input( "Enter the decimal representation of Minterms 'Spaces Separated'\n" ).split() ] binary = decimal_to_binary(no_of_variable, minterms) prime_implicants = check(binary) print("Prime Implicants are:") print(prime_implicants) chart = prime_implicant_chart(prime_implicants, binary) essential_prime_implicants = selection(chart, prime_implicants) print("Essential Prime Implicants are:") print(essential_prime_implicants) if __name__ == "__main__": import doctest doctest.testmod() main()