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kmap_solver.py
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kmap_solver.py
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# K-Map Minimization
# Name: ANKIT MISHRA
# Date: 16/10/2018
def minFunc(numVar, stringIn):
num= int(numVar)
x= stringIn
"""
This python function takes function of maximum of 4 variables
as input and gives the corresponding minimized function(s)
as the output (minimized using the K-Map methodology),
considering the case of Don’t Care conditions.
Input is a string of the format (a0,a1,a2, ...,an) d(d0,d1, ...,dm)
Output is a string representing the simplified Boolean Expression in
SOP form.
"""
l= []
i=0
while(x[i]!='d'):
if(x[i].isdigit()==True): # taking the values from the input, and storing it in a list
if(x[i+1].isdigit()==False):
l.append(x[i])
i+=1
else:
l.append(x[i]+x[i+1])
i+=2
else:
i+=1
y=i
ess=list(l) #storing essential prime implicant in a seprate list for further use
if(x[y+1]!='-'):
while(x[y]!=')'):
if(x[y].isdigit()==True):
if(x[y+1].isdigit()==False): #storing the dont care condition giving in the input
l.append(x[y])
y+=1
else:
l.append(x[y]+x[y+1])
y+=2
else:
y+=1
if(num==4):
for i in range(len(l)): #converting to binary for 4 variables
l[i] = format(int(l[i]), '04b')
elif(num==3):
for i in range(len(l)): #converting to binary for 3 variables
l[i] = format(int(l[i]), '03b')
elif(num==2):
for i in range(len(l)): #converting to binary for 2 variables
l[i] = format(int(l[i]), '02b')
a,b,c,d,e,f,g,h,p,q,w,r,t,y,m,n,o,z,u,v = [],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[],[] #creating list to be stored
l.sort()
count = 0
t=0
# Quine-McCluskey and Petrick methods -
for i in range(len(l)):
for j in range(num): #Storing the digit speratly on the basis of much many 1's they contain
if(l[i][j]=='1'):
count+=1
if(count==0):
a.append(l[i])
if(count==1): #appending into one of the list created above for seperation
b.append(l[i])
if(count==2):
c.append(l[i])
if(count==3):
d.append(l[i])
if(count==4):
e.append(l[i])
count=0
def step1(a,b,f): # Proceding tp step 1 comparing a and b then follows on uptil all thrr couples are compared
count=0
for i in range(len(a)):
for k in range(len(b)): #loops
for j in range(num):
if(a[i][j]!=b[k][j]):
count+=1
if(count==1):
for j in range(num):
if(a[i][j]!=b[k][j]):
f.append(str(str(a[i][:j])+'x'+str(a[i][j+1:])+',('+str(int(a[i],2))+','+str(int(b[k],2))+')')) #slicing and appending
count=0
return(f)
f=step1(a,b,f) #calling the function and storing what it returns
g=step1(b,c,g)
h=step1(c,d,h)
p=step1(d,e,p)
def step2(f,g,q):
count=0
for i in range(len(f)): #same as step 1 , step 2 does the same on the output of step 1 and give us a compariable impicants
for k in range(len(g)):
for j in range(num):
if(f[i][j]!=g[k][j]): #loops
count+=1
if(count==1):
for j in range(num):
if(f[i][j]!=g[k][j]):
q.append(str(str(f[i][:j])+'x'+str(f[i][j+1:-1])+','+ str(g[k][num+2:]))) #slicing and appending
count=0
return(q)
q = step2(f,g,q) #calling the function and storing what it returns
w = step2(g,h,w)
r = step2(h,p,r)
def step3(f,g,q):
count=0
for i in range(len(f)): #same as step 2 , step 3 does the same on the output of step 2 and give us a compariable impicants
for k in range(len(g)):
for j in range(num):
if(f[i][j]!=g[k][j]):
count+=1 #loops
if(count==1):
for j in range(num):
if(f[i][j]!=g[k][j]):
q.append(str(str(f[i][:j])+'x'+str(f[i][j+1:-1])+ ',' +str(g[k][6:]))) #slicing and appending
count=0
return(q)
m = step3(q,w,m) #calling the function and storing what it returns
n = step3(w,r,n)
def step4(f,g,p):
count=0
for i in range(len(f)): #same as step 3 , step 4 does the same on the output of step 3 and give us a compariable impicants
for k in range(len(g)):
for j in range(num):
if(f[i][j]=='x'): #loops
if(g[k][j]=='x'):
count+=1
if(count==2):
for j in range(num):
if(f[i][j]!=g[k][j]):
p.append(str(str(f[i][:j])+'x'+str(f[i][j+1:-1])+ str(g[k][-4:]))) #slicing and appending
count=0
return(p) #return
o = step4(m,n,o) #fuction calling
z=list(o)
if(len(z)==0):
z=list(m)
z.extend(n) # getting the last unempty ist so that we can have the prime implicants stored in a particular list
if(len(z)==0):
z=list(q)
z.extend(w)
z.extend(r)
if(len(z)==0):
z=list(f)
z.extend(g)
z.extend(h)
z.extend(p)
if(len(z)==0):
z=list(a)
z.extend(b)
z.extend(c)
z.extend(d)
z.extend(e)
def concatinate(q): #concatinating the list of unneccesary repeatation of the implicants
for i in range(len(q)):
for k in range(1+i,len(q)):
if(q[i][:num]==q[k][:num]):
q[k] = ''
while '' in q:
q.remove('')
return(q) #return
z = concatinate(z)
if ")" in z[0]: #function call
def left(q): #getting whats left in quine method of table and storing it in another list
for i in range(len(q)):
j=num+1
while(q[i][j]!=')'):
if(q[i][j].isdigit()==True):
if(q[i][j+1].isdigit()==False):
u.append(q[i][j])
j+=1
else:
u.append(q[i][j]+q[i][j+1])
j+=2
else:
j+=1
return(u) #return
u=left(z) #fucntion call
def simple(u): #removing repeated entries
for i in range (len(u)):
for k in range(i+1,len(u)):
if(u[i]==u[k]):
u[k]=''
while '' in u:
u.remove('')
return(u) #return
u=simple(u) #function call
# Further code deals with the dont care conditions and isnt neccssary if you want to simplify it further it adds up to beauty.
def dcare(f,u,v):
count=0
for i in range(len(f)):
j=5 #to find out whats left, for loop run all over
while(f[i][j]!=')'):
if(f[i][j].isdigit()==True):
if(f[i][j+1].isdigit()==False):
if(f[i][j] not in u):
count+=1 #loops
u.append(f[i][j])
j+=1
else:
if(f[i][j]+f[i][j+1] not in u):
count+=1
u.append(f[i][j]+f[i][j+1])
j+=2
else: #else condition
j+=1
if(count>=1):
v.append(f[i])
count=0
return(v,u)
def acare(a,b,c,d,e,v):
if(len(a)==0 and len(c)==0):
v.extend(b) #checking the left over in the very first seperation table
if(len(b)==0 and len(d)==0):
v.extend(c)
if(len(c)==0 and len(e)==0):
v.extend(d)
if(len(d)==0):
v.extend(e)
for i in range(len(v)):
v[i]=str(int(v[i],2)) #converting to decimal in returning the value
return(v)
v=acare(a,b,c,d,e,v)
v,u=dcare(n,u,v)
v,u=dcare(m,u,v)
v,u=dcare(r,u,v) #checking each step of the quine table for left over elements
v,u=dcare(w,u,v)
v,u=dcare(q,u,v)
v,u=dcare(p,u,v)
v,u=dcare(h,u,v)
v,u=dcare(g,u,v)
v,u=dcare(f,u,v)
v=concatinate(v)
z.extend(v)
#storing all implicants including dont care in the same list
def order(z):
for i in range(len(z)):
count=0
count1=0
for j in range(num):
if(z[i][j]=='x'):
count1+=1
a=num+1
while(z[i][a]!=')'):
if(z[i][a].isdigit()==True):
if(z[i][a+1].isdigit()==False):
if z[i][a] in ess:
count+=1
a+=1
else:
if((z[i][a]+z[i][a+1]) in ess):
count+=1
a+=2
else:
a+=1
if(count==(2*count1)):
temp = z[0]
z[0]=z[i]
z.pop(i)
z.insert(1,temp)
return(z)
z=order(z)
def imp(z):
prime=[]
for i in range(len(z)):
count=0
j=num+1
while(z[i][j]!=')'):
if(z[i][j].isdigit()==True):
if(z[i][j+1].isdigit()==False):
if z[i][j] in ess:
count+=1
ess.remove(z[i][j])
j+=1
else:
if((z[i][j]+z[i][j+1]) in ess):
count+=1
ess.remove((z[i][j]+z[i][j+1]))
j+=2
else:
j+=1
if(count>=1):
prime.append(z[i])
return(prime)
z=imp(z)
# Expresing the prime implicants in the form of 4 variables
def exp(z):
if(num==4):
dir = {0:'abcd',1:'abcz',2:'abyd',3:'abyz',4:'axcd',5:'axcz',6:'axyd',7:'axyz',8:'wbcd',9:'wbcz',10:'wbyd',11:'wbyz',12:'wxcd',13:'wxcz',14:'wxyd',15:'wxyz'}
elif(num==3):
dir = {0:'abc',1:'aby',2: 'axc',3:'axy',4:'wbc',5:'wby',6:'wxc',7:'wxy'} #Dictionary
elif(num==2):
dir = {0:'ab',1:'ax',2: 'wb',3:'wx'}
f=''
if ')' in z[0]:
for i in range(len(z)):
s=[] #loops
j=num+1
while(z[i][j]!=')'):
if(z[i][j].isdigit()==True):
if(z[i][j+1].isdigit()==False):
s.append(dir[int(z[i][j])]) #string appending
j+=1
else:
s.append(dir[int(z[i][j]+z[i][j+1])])
j+=2
else:
j+=1
for j in range(num):
count=0
for k in range(0,len(s)-1):
if(s[k][j]==s[k+1][j]): #adding up the variable to create expression
count+=1
if(count==(len(s)-1)):
if(s[k][j]=='a'):
f=f+'w\''
elif(s[k][j]=='b'):
f=f+'x\''
elif(s[k][j]=='c'):
f=f+'y\''
elif(s[k][j]=='d'):
f=f+'z\''
else:
f=f+s[k][j]
if(i!=(len(z)-1)):
f=f+'+'
else:
s=[]
decimal =0
for i in range(len(z)):
for digit in z[i]:
decimal = decimal*2 + int(digit)
z[i]=decimal
decimal=0
for i in range(len(z)):
s.append(dir[(z[i])])
for i in range(len(s)):
for j in range(len(s[i])):
if(s[i][j]=='a'):
f=f+'w\''
elif(s[i][j]=='b'):
f=f+'x\''
elif(s[i][j]=='c'):
f=f+'y\''
elif(s[i][j]=='d'):
f=f+'z\''
else:
f=f+s[i][j]
if(i!=(len(z)-1)):
f=f+'+' #SOP operator
return(f)
stringOut=exp(z) #storing
return (stringOut) #returning the K map value back
'''Samples to test if the code works properly or not'''
print(minFunc('2','(1,2)d-'))
print(minFunc('3','(2,5)d(0,4,6)'))
print(minFunc('4','(3,9,12,15)d(0,1,4,7,8,10,11,14)'))
print(minFunc('4','(1,2,4,5,6,10,11,12,13)d-'))