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)

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     |
---------------------------

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