I was asked the following question:

Write the VHDL assignment operator for the Y2 output (most significant bit) of a BCD-to-binary encoder. Use Boolean operators, D0-D9 as the data inputs lines, and Y0-Y2 for the outputs. Inputs and outputs are active-HIGH. Please note that ONLY one VHDL statement is needed, don't write a whole program.
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I am having several problems with this question:

• First, wouldn't this need a Y3 to be able to represent all decimal digits?
• Second, in that case, Y3 would be the most significant bit, right?

When I brought up these questions, I got the response:

If we have 10 input lines, which is 2^3 = 8 < 10 < 2^4 = 16. That means, we can use either 3 or 4 output lines. We have chosen 3 output lines in this case.
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But this doesn't make sense to me either. You can only "choose" 3 output lines if you don't want to represent 8, 9 and 10, right?

Can somebody clarify this for me? Thanks in advance!

 

Using 10 bits, you can represent 399 (decimal) in BCD. No, the question doesn't make sense.