Rules: Closed book and notes. No calculator is allowed. Show all your work for full credit, using the standard methods. Please draw and write NEATLY (If I cannot read it, I must mark it WRONG). Do all work and put all answers on YOUR paper, not this sheet. Give a single answer, enclosed in a box if it's an equation or expression, to each question. Keep your work and the associated answer together, and carefully label them with the problem number and part number. Use only one side of the paper.
1. [25 pts] Draw a standard Karnaugh map and use it to find the minimal sum-of-products equation for the following function. Clearly indicate the distinguished one cells.
2. [25 pts] A control system measures the brightness of a widget and represents it as a 3-bit unsigned binary number. Design a circuit that evaluates this brightness code and outputs a signal that shoves the widget into a bin if the brightness is in the range of 3 to 5 (decimal); otherwise it does not shove it.
3. [25 pts] Analyze the following logic diagram and derive an SOP equation.
4. [25 pts] Use the boolean axioms and/or theorems to prove the following equation. Write the corresponding theorem or axiom, in its standard form, adjacent to each step of your proof.
