Twos Complement

Design a circuit (called TWOS_COMP) that takes a 4-bit input (A3-A0, where A0 is the least significant bit) and produces a 4-bit output (B3-B0, where B0 is the least significant bit), such that the resulting output bits are the result of applying the twos complement operation (described in the lecture) on the input bits.

Steps required:

1. Create a truth table for all possible 4-bit inputs, and use your understanding of twos complement to fill in the values for the output bits.
2. Create an un-simplified sum-of-products expression for this truth table.
3. Use either a Karnaugh map (recommended) or Boolean algebraic simplification to simplify this expression into the simplest sum-of-products form.
4. Create a circuit using this simplified sum-of-products expression.