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Parity Bit

  1. Oct 19, 2014 #1
    1. The problem statement, all variables and given/known data
    A parity bit will be 0 if the data contains an
    even number of 1’s and it will be 1 if the data contains an odd number of 1’s. If during
    transmission a 1 is changed to a 0 or vice versa, then the parity check at the receiver will
    fail. Determine the parity P for
    4–bits of data, A, B, C, and D. You should
    Determine the truth table, Karnough Map, and logical expression for P. Draw the circuit that executes the logic. Simplify the circuit to a minimum number of logic gates.

    2. Relevant equations


    3. The attempt at a solution
    Would the solution just be an even parity? In that case.

    Truth Table: Since it is 0 with an even number 1s, and 1 if it will has an odd number of 1s
    4-bit | Parity
    0000 0
    0001 1
    0010 1
    0011 0
    0100 1
    0101 0
    0110 0
    0111 1
    1000 1
    1001 0
    1010 0
    1011 1
    1100 0
    1101 1
    1110 1
    1111 0

    Karnough Map:
    For AB on the column and CD on the row

    -----00 01 11 10
    00--0--1---0---1
    01--1--0--1----0
    11--0--1--0----1
    10--1--0--1---0

    Logical Expression:
    P =A ⊕ B ⊕ C ⊕ D

    Never really been taught how to come up with the circuit diagram though. Any help?

     
  2. jcsd
  3. Oct 20, 2014 #2

    CWatters

    User Avatar
    Science Advisor
    Homework Helper

    Perhaps start with the logic symbol for a ⊕ gate?
     
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