Qn: Simplify the following functions, and implement them with two-level NOR gate circuits: (a) F=wx′+y′z′+w′yz′ (b) F(w,x,y,z)=Σ(0,3,12,15) (c) F(x,y,z)=[(x+y)(x=z)]′

**ANS**:

**Function (a): F=wx’+y’z’+w’yz’**

Simplified form: F = (y’ + w’)(z’ + w’)

Two-level NOR gate circuit implementation:

```
------------------
| NOR | NOR |
| | |
| y' | w' |
| | |
| --- | --- |
| | |
| z' | w' |
| | |
| --- | --- |
| | |
| y | w |
| | |
| NOR | NOR |
------------------
```

**Function (b): F(w,x,y,z)=Σ(0,3,12,15)**

Simplified form: F = w’x’y’ + w’xz’ + wxy’ + wxyz

Two-level NOR gate circuit implementation:

```
-----------------------------------------
| NOR | NOR | NOR | NOR |
| | | | |
| w' | x' | y' | w |
| | | | |
| --- | --- | --- | --- |
| | | | |
| wx'y' | wxz' | wxy' | wxyz |
| | | | |
| NOR | NOR | NOR | NOR |
| | | | |
| wx | wx | wy | wz |
| | | | |
| --- | --- | --- | --- |
| | | | |
| wxy | wxz | wyz | wzz |
| | | | |
| NOR | NOR |
| | |
| wy'z | wz'z |
-----------------------------------------
```

**Function (c): F(x,y,z)=[(x+y)(x=z)]’**

Simplified form: F = (x’ + y’)(xy + x’z’)

Two-level NOR gate circuit implementation:

```
---------------------------
| NOR | NOR |
| | |
| x' | y' |
| | |
| --- | --- |
| | |
| x | y |
| | |
| NOR | NOR |
| | |
| x'z' | xy |
---------------------------
```