Two-Level NOR circuit

Discussion in 'Homework Help' started by Voltboy, Feb 2, 2012.

  1. Voltboy

    Thread Starter Active Member

    Jan 10, 2007
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    0
    Hello,
    For a homework I have to implement diferent circuits with AND, NOR, NAND, OR using two-level implementation and using real 2-input implementation. I've figured how to do this for all gates except NOR.
    For all gates except NOR the following applies:
    2-level implementation=2-input implementation
    X (gate) Y (gate) Z = (X(gate)Y) (gate) Z

    but
    X (NOR) Y (NOR) Z ≠ (X(NOR)Y) (NOR) Z

    how would I go from a 2-input NOR circuit to a 2-level (possibly 3 input NOR) circuit? i.e from the left hand side to an equivalent right hand side.

    Thanks.
     
  2. Georacer

    Moderator

    Nov 25, 2009
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    1,266
    It's the exact same thing you did for NAND. What was your method there?
     
  3. Voltboy

    Thread Starter Active Member

    Jan 10, 2007
    197
    0
    I used the bubble approach, and that works for NAND and NOR but you end up with a 2-input implementation of the circuit. Changing the 2-input NAND implementation to 2-level NAND implementation is easy because as I said:
    ((X NAND Y) NAND z) is the same as a single 3-input NAND gate (X NAND Y NAND Z)
    but ((X NOR Y) NOR Z) is not the same as a 3-input NOR gate.
     
  4. Georacer

    Moderator

    Nov 25, 2009
    5,142
    1,266
    Actually, NAND(x,y,z) isn't the same as (x NAND y) NAND z.

    In the first case, the test input 111 gives a correct results of 0.
    In the second case, the same input gives:
    (1 NAND 1) NAND 1=
    0 NAND 1=
    1
    which is wrong.

    You need to add an extra gate to the first level, to "condition" the single input y. Think about it like passing it through a 1-input NAND gate.

    The same applies to the NOR implementation.
     
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