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.

Question

11-10-2016
Computers and Technology

Answered

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.

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isaacholton7 isaacholton7 · Answer 1 · 2016-10-11T13:56:49-04:00

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 = A3A2 + A3A1
Finally just draw or connect the circuit using NAND