def num2term(num, vs, conj=False):
"""Return a tuple of all variables for a given term index.
Parameters
----------
num: int
vs: [Variable]
conj: bool
conj=False for minterms, conj=True for maxterms
Examples
--------
Table of min/max terms for Boolean space {a, b, c}
+-----+----------+----------+
| num | minterm | maxterm |
+=====+==========+==========+
| 0 | a' b' c' | a b c |
| 1 | a b' c' | a' b c |
| 2 | a' b c' | a b' c |
| 3 | a b c' | a' b' c |
| 4 | a' b' c | a b c' |
| 5 | a b' c | a' b c' |
| 6 | a' b c | a b' c' |
| 7 | a b c | a' b' c' |
+-------+----------+----------+
"""
if conj:
return tuple(-v if bit_on(num, i) else v for i, v in enumerate(vs))
else:
return tuple(v if bit_on(num, i) else -v for i, v in enumerate(vs))
def decode(self):
"""Return symbolic logic for an N-2^N binary decoder.
Example Truth Table for a 2:4 decoder:
+===========+=====================+
| A[1] A[0] | D[3] D[2] D[1] D[0] |
+===========+=====================+
| 0 0 | 0 0 0 1 |
| 0 1 | 0 0 1 0 |
| 1 0 | 0 1 0 0 |
| 1 1 | 1 0 0 0 |
+===========+=====================+
>>> A = bitvec('a', 2)
>>> d = A.decode()
>>> d.vrestrict({A: "00"})
[1, 0, 0, 0]
>>> d.vrestrict({A: "10"})
[0, 1, 0, 0]
>>> d.vrestrict({A: "01"})
[0, 0, 1, 0]
>>> d.vrestrict({A: "11"})
[0, 0, 0, 1]
"""
items = [ And(*[ f if bit_on(i, j) else -f
for j, f in enumerate(self) ])
for i in range(2 ** len(self)) ]
return self.__class__(items)
def factor(self, conj=False):
obj = self if self._simplified else self.simplify()
if obj in B:
return obj
elif isinstance(obj, Exclusive):
outer, inner = (And, Or) if conj else (Or, And)
args = list()
for n in range(1 << len(obj.args)):
if parity(n) == obj.PARITY:
term = [arg.factor(conj) if bit_on(n, i) else Not(arg).factor(conj)
for i, arg in enumerate(obj.args)]
args.append(inner(*term))
return outer(*args)
else:
return obj.factor(conj)
def num2point(num, vs):
"""Convert a number to a point in an N-dimensional space."""
return {v: bit_on(num, i) for i, v in enumerate(vs)}
