I'm currently working on a project for my course. I have to design a logic system that when a 4-bit binary input is entered, the circuit produces a HIGH (logic 1) output under the following cirumstances:

- The input is less than or equal to 2 (decimal)

- The input is greater than or equal to 10 (decimal)

I'd really like some feedback to make sure that I'm on the right track.

Here is what I have so far:

1) Truth Table

From this, I can deduce the following Boolean logic functions. I'm going to use "*" to denote the NOT operator.

A*B*C*D*

A*B*C*D

A*B*CD*

AB*CD*

ABC*D*

ABC*D

ABCD*

ABCD

Righto, so we can assume the Output = 1 if

A*B*C*D* + A*B*C*D + A*B*CD* + AB*CD* + ABC*D* + ABC*D + ABCD* + ABCD

Now, I have to simplify this expression as much as possible. Then I have to implement the design using NAND gates only.

I can use any number of the following Integrated Circuits:

- 4 x 2 Input NANDs

- 3 x 3 Input NANDs

- 2 x 4 Input NANDs

So, before I work on simplifying all the expression, am I on the right track? Thanks.