Truth table of a BCD-to-binary priority encoder.?

Question

Hi all,
I found a problem from Logic and Computer Design, Mano, that I can't solve.
The problem is short:
Derive the truth table of a BCD-to-binary priority encoder.

Can someone please help me out? :)

Thanks

Josh

Answer 1

If I understand you correctly you want the BCD to have priority Inputs...
A priority encoder only processes the highest input bit and ignores the rest.

Consider the following 8 bit priority input (Left bits are LSB) For regular binary
Input Output Idle
00000000........XXXX... 1
10000000........0000.....0
X1000000........0001.....0
XX100000........0010....0
XXX10000........0011....0
XXXX1000........0100....0
XXXXX100........0101....0
XXXXXX10.......0110.....0
XXXXXXX1......0111.....0

Notice that the highest bit(rightmost) that is set(1) causes the lower bits to be ignored. There is an idle state which is set when no inputs are set. The above truth table has 8 bits of an input and its output value ranges from 000 (zero) to 111(7) eight distinct states, one for each bit position of the binary input.

BCD (binary coded decimal) uses 4 bit position to represent the decimal numbers 0 to 9. Even though the 4 binary numbers can represent decimal 0 to 15 , any value above 9 is not used in BCD

So a single BCD digit has four bits and ranges from 0000 to 1001 in binary.

To prioritize BCD inputs you will only have 4 bits per digit
Since my truth table above has the lowest significant bit on the left the number 47 would be represented in BCD as
01111000 where:
4 = 1000
7 = 0111

This would correspond to a prioritized input as
XXXX1000 with an output of 0100

Answer 2

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If you use negative logic, where 1 is false and 0 is true. Then D C B A -- Decimal -- since 1 1 1 1 -- -- 0 ---- FFFF 1 1 1 0 -- -- 1 -- -- FFFT 1 1 0 1 -- -- 2 -- -- FFTF 1 1 0 0 -- -- 3 -- -- FFTT 1 0 1 1 -- -- 4 -- -- FTFF 1 0 1 0 -- -- 5 -- -- FTFT 1 0 0 1 -- -- 6 -- -- FTTF 1 0 0 0 -- -- 7 -- -- FTTT 0 1 1 1 -- -- 8 -- -- TFFF 0 1 1 0 -- -- 9 -- -- TFFT Remember this is a priority encoder with 9 being the highest priority down to 1 the lowest priority.