I am so confused on this problem. We are given a function $f$ and told to design a circuit that has four inputs labeled $b_3,...,b_0$, and an output $f$, where $f = 1$ if the 4-bit input pattern is a valid BCD digit; otherwise $f = 0$. We want to use minimum cost implementation.
Here is the function: $f = b_3b_0 + \bar b_2 b_1b_0 + b_2b_1 \bar b_0$
I am confused on how to design this with minimum cost. So my circuit will obviously need to be able to perform AND, OR, and NOT.
Here is what I am coming up with, but I don't think it is right by any means: https://gyazo.com/cb9fffc430c03c25c55dd962e943cea1
My circuit makes use of seemingly way too many components for this to be correct. Can anyone help?