quine mc cluskey Algorithm
The Quine – McCluskey algorithm (QMC), also known as the method of prime implicants, is a method used for minimization of Boolean functions that was developed by Willard V. Quine in 1952 and extended by Edward J. McCluskey in 1956.Use those prime implicants in a prime implicant chart to find the essential prime implicants of the function, as well as other prime implicants that are necessary to cover the function.
def compare_string(string1, string2):
"""
>>> compare_string('0010','0110')
'0_10'
>>> compare_string('0110','1101')
-1
"""
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 -1
else:
return "".join(l1)
def check(binary):
"""
>>> check(['0.00.01.5'])
['0.00.01.5']
"""
pi = []
while 1:
check1 = ["$"] * len(binary)
temp = []
for i in range(len(binary)):
for j in range(i + 1, len(binary)):
k = compare_string(binary[i], binary[j])
if k != -1:
check1[i] = "*"
check1[j] = "*"
temp.append(k)
for i in range(len(binary)):
if check1[i] == "$":
pi.append(binary[i])
if len(temp) == 0:
return pi
binary = list(set(temp))
def decimal_to_binary(no_of_variable, minterms):
"""
>>> 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, string2, count):
"""
>>> 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, prime_implicants):
"""
>>> 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, binary):
"""
>>> 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():
no_of_variable = int(input("Enter the no. of variables\n"))
minterms = [
int(x)
for x in input(
"Enter the decimal representation of Minterms 'Spaces Seprated'\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()
