digital logic

Question

Consider a circuit which converts a BCD code to a 2421 code.The size of the decoder needed to implement the circuit is ______.

Answer 1

BCD Code is used to represent the 10 decimal numbers and in order to represent 10 numbers, we need atleast 4 binary digits. If size of input in decoder is n , output will be 2ⁿ.

So for 4 inputs, we get 16 outputs . Out of these 16 outputs, only 10 outputs correspond to the 2-4-2-1 representation of the corresponding BCD representation. Rest are don't care terms. 

Refer to the below diags for  table and decoder circuit :