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BCD to Gray Code Converter

  1. May 9, 2015 #1
    Having a bit of trouble understanding why there are two different truth tables for BCD to Gray.

    Using ABCD as the BCD and WXYZ as the Gray,
    The way I learned it is:
    1) MSB of BCD (A) = MSB of Gray (W)
    2) A ⊕ B = X
    3) B ⊕ C = Y
    4) C ⊕ D = Z
    5) Since BCD only ranges from 0 - 9, 10 - 15 become "don't cares"

    Following the rules, chart prints:

    However, while browsing through examples of converting BCD to Gray, I found these:
    Example Problem
    Example Problem 2

    The rules I posted don't work in the Example Problems.

    Are there some sort of exceptions that may alter the Gray Code?
    Last edited: May 9, 2015
  2. jcsd
  3. May 9, 2015 #2


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    There are at least 3 different BCD-codes:


    Maybe that's the cause to confusion?

    But why not choose the one you like, practise some Karnough mapping and make your own truth table ?

    Observe: BCD4221(5) is wrong: It must be 1001 or 0111
    Last edited: May 9, 2015
  4. May 9, 2015 #3
    Thanks for the reply,

    The problem I'm facing requires me to,
    "implement a BCD to Gray Code converter using a 4x16x4 PAL where each output collects 4 different product terms."

    I completed the problem using the 8421 BCD code to Gray, but the solutions solved it the way shown here: Example Problem
    Would using the 8421 BCD to Gray functions where
    W = A
    X = A'B
    Y = A'BC' + B'C
    Z = A'BC'D + B'C'D + AD + BCD + B'CD'

    be considered correct in this problem still? I'm skeptical regarding my answer since the question requested "output collects 4 different product terms." I'm assuming that part just means the OR gates in the PAL needs to collect 4 connections from the AND gates.
    Last edited: May 9, 2015
  5. May 10, 2015 #4


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    The rules here:
    matches the BCD and gray-codes here:


    In your examples in #1, there are other gray-codes, and of course your rules will not match these.

    For example, how have you found: Z = A'BC'D + B'C'D + AD + BCD + B'CD' in #3 ? That's not right.
  6. May 10, 2015 #5
    Yeah that's not right.
    Re-did the K-Map and found Z = A'C'D + B'C'D + A'CD'

    But how would you solve the problem in the example using their BCD-Gray Code instead of the 8421 choice?
    Certainly the rules will not work in that.
  7. May 10, 2015 #6


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    I cannot find out what you are doing. Which BCD-code and which gray-code ar you using?

    As for the BCD- and gray-codes shown in #4, the result is:

    Z = C ⊕ D = ( C * !D ) + ( !C * D )

    ( ! means "not" )
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