Question

A BCD code is being transmitted to a remote receiver. The bits are A3, A2, A1, and A0, with A3as the MSB. The receiver circuitry includes a BCD error detector circuit that examines the received code to see if it is a legal BCD code (i.e., ≤1001). Design this circuit to produce a HIGH for any error condition.

Answer 1

BCD only goes from digit 0 (0000) to digit 9 (1001), because for 10 you need two digits, so all you've got to do is make a function that produces high for numbers from 10 (1010) to 15 (1111) as follows:
A3 A2 A1 A0 F
0 0 0 0 0
0 0 0 1 0
0 0 1 0 0
...........................
1 0 0 0 0
1 0 1 0 1
1 0 1 1 1
1 1 0 0 1
1 1 0 1 1
1 1 1 0 1
1 1 1 1 1

Then simplify the function: F = A3*A2 + A3*A1 Finally just draw or connect the circuit using NAND