Logic gate in Matrix representation?

Discussion in 'General Electronics Chat' started by yzc717, Nov 5, 2010.

  1. yzc717

    Thread Starter New Member

    Nov 5, 2010
    2
    0
    the logic gate not, and, or gate in matrix representation, I have no idea how they works, and why they are drew in this way, google it give me no luck, anyone know about it? further explaination appreciated.

    Not gate:
    01
    10

    And gate:
    1110
    0001

    Not gate:
    1000
    0111
     
  2. nomurphy

    AAC Fanatic!

    Aug 8, 2005
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  3. swenaac

    New Member

    Jul 27, 2016
    1
    0
    If one-bit state is represented by
    0 = [ 1 0 ]'
    1 = [ 0 1 ]'
    and two-bit state is represented by the following vector or 4x1 matrices (similar to quantum mechanics)
    00 = [ 1 0 0 0 ]'
    01 = [ 0 1 0 0 ]'
    10 = [ 0 0 1 0 ]'
    11 = [ 0 0 0 1 ]'
    then an AND gate can be represented by a 2x4 matrix:
    1 1 1 0
    0 0 0 1

    It's easy to verify gate_matrix x 2bit_state_matrix = 1bit_state_matrix.

    Other logic operation gates include:
    NAND:
    0 0 0 1
    1 1 1 0
    OR:
    1 0 0 0
    0 1 1 1
    NOR:
    0 1 1 1
    1 0 0 0
     
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