digital-logic - w'xz + w'yz + x'yz' + wxy'z 如何用 4 个 NOR 门（+ 反相器）来实现，给定 d = wyz

Question

如何仅用四个 NOR 门和反相器实现以下功能：

F = w'xz + w'yz + x'yz' + wxy'z

d = wyz

Answer 1

首先得到卡诺图：

w’x z + w’ yz +  x’yz’ + wxy’z
a       b         c      d

wx\yz 00  01  11  10

            ----   c
00    0   0 | 1| |1 |
            | b| ----
        ----|----
01    0 |a1 | 1|| 0
        ----|--|-
            ---
11    0   1d  0   0 
                 
                 ---
10    0   0   0  |1 |

然后得到总和的乘积：

wx\yz 00  01  11  10

    |      |
    |      |
00  | 0   0|   1   1 
    --------
            
  ------         -------
01    0|  1    1 | 0
       |         |   A
       |      ---|
11    0|  1   |0|| 0 
  ------      |C|--------
   --------   | |  
10 |  0   0|  |0|  1
   |       |  ---
   |       |
   |  B    |
 
(x'+z)(x+y')(w'+y'+z')
  A      B       C

然后减少以利用可用的 d 引脚，并获得请求的 4 个 nors：

=((x'+z)(x+y')(w'+y'+z'))''
=(((x'+z)(x+y'))(w'+y'+z'))''
=(((x'+z)(x+y'))'+(w'+y'+z')')'
=(((x'+z)(x+y'))'+(wyz))'
=(((x'+z)(x+y'))'+d)'
=(((x'+z)'+(x+y')')+d)'
=(((x'+z)'+(x+y')')''+d)'
         ^       ^ ^    ^  4 nors
     ^         ^    ^      3 nots or nands are also needed