Electronic – A circuit to convert 4-bit Gray numbers to BCD

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I'm sorry for asking this specific question here but can some one please tell me what's wrong with this solution.

Question: design a circuit to convert 4bit Gray numbers to BCD enter image description here

I have to say I wrote numbers in Gray form in the left hand side of the truth table.

Let's consider a number such 1000 in Gray

My solution:

It's binary equivalent is 1111 and we cannot show that in BCD so output have to be don't care

Here is what my professor says:

Binary equivalent: 1111

Decimal equivalent: 15

BCD equivalent:00010101

I'm completely confused 😐

Edit:

As some users noted I wrote grey codes in non sequential order.

But the answer of karnaugh map will remain same. To see this you can compare the link @Jack Creasey added as comment and my karnaugh maps.(also note I just designed this circuit with decoder)

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Best Answer

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The Answer requires;

  • Binary to Gray ( correct your errors)
  • 4 bit Gray to 5 bit BCD or {B8=0,B7=0,B6=0,B5}{B4,B3,B2,B1}
  • 5 bit BCD in 5 Karnaugh Maps then reduce each
  • 5 Maps to 5 logic symbol circuits to complete design, 1 for each 5 bit gray,

Perhaps 10/20 is generous.

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