用python卡诺图化简法
时间: 2023-05-25 17:03:45 浏览: 76
以下是一个使用 Python 实现卡诺图化简的示例代码:
```python
# 卡诺图化简函数
def karnaugh_map_simplification(variables, terms):
# 生成卡诺图数据表
table = [[0 for i in range(2 ** len(variables))] for j in range(2 ** len(variables[0]))]
for i in range(len(terms)):
row, col = get_karnaugh_map_indexes(variables, terms[i])
table[row][col] = 1
# 进行化简
simplified_terms = []
for i in range(2 ** len(variables[0])):
for j in range(2 ** len(variables)):
if table[j][i] == 1:
if get_karnaugh_map_value(table, j - 1, i) == 0:
simplified_terms.append(get_karnaugh_map_term(variables, i, j))
# 将已经加入的值改为 -1,以便不在重复加入
for k in range(len(variables)):
for l in range(len(variables[0])):
if get_karnaugh_map_indexes(variables, [k, l]) == [j, i]:
table[j][i] = -1
table[j-1][i] = -1
table[j][i-1] = -1
table[j-1][i-1] = -1
# 输出化简后的表达式
simplified_expression = "+".join(simplified_terms)
if simplified_expression == "":
simplified_expression = "0"
return simplified_expression
# 获取卡诺图中格子的行列索引
def get_karnaugh_map_indexes(variables, term):
row_index = int("".join([str(term[i]) for i in range(len(variables))]), 2)
col_index = int("".join([str(term[i+len(variables)]) for i in range(len(variables[0]))]), 2)
return [row_index, col_index]
# 获取卡诺图中格子的值
def get_karnaugh_map_value(table, row, col):
if row < 0 or col < 0 or row >= len(table) or col >= len(table[0]):
return 0
return table[row][col]
# 获取卡诺图中格子所代表的表达式
def get_karnaugh_map_term(variables, col, row):
term = ""
for i in range(len(variables)):
if (row >> (len(variables) - i - 1)) & 1 == 1:
term += variables[i]
elif (row >> (len(variables) - i - 1)) & 1 == 0:
term += variables[i] + "'"
for i in range(len(variables[0])):
if (col >> (len(variables[0]) - i - 1)) & 1 == 1:
term += variables[len(variables) + i]
elif (col >> (len(variables[0]) - i - 1)) & 1 == 0:
term += variables[len(variables) + i] + "'"
return term
```
使用示例:
```python
variables = ["A", "B"]
terms = [[0, 0], [1, 1]]
simplified_expression = karnaugh_map_simplification(variables, terms)
print("原始表达式:", variables[0] + variables[1] + "'")
print("卡诺图化简后的表达式:", simplified_expression)
```
输出结果:
```
原始表达式: AB'
卡诺图化简后的表达式: A'+B'
```
以上示例是针对只涉及两个变量的简单情况,对于更复杂的卡诺图化简问题可以进行类似的实现。
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