Test 2 CMSC 2100 Fall 2025

Name ______________________________________

• Please answer each question fully, carefully and thoughtfully.
• No credit will be given for unreadable answers, please write neatly.
• Answer the questions in any order, but please number each answer.
• Put your name on the top of this page and staple it to your answers.
• Please show all computations.
  • You may use a calculator, but write down intermediate steps
  • The purpose of the questions is to demonstrate an algorithm or technique. If you do not show your computations, the answer will be marked incorrect.

1. [9 points] Provide the truth table, expression and circuit symbol for a and b
   
2. [2 points] Use a truth table to proved a+0 = a
   
3. Transistors and Circuits
   1. [5 points] Describe the relationship between transistors and the basic gates.
   2. [5 points] Why is it reasonable to say that more transistors lead to faster computers?

4. Represent the following as

   a	b	c	F
   0	0	0	0
   0	0	1	1
   0	1	0	0
   0	1	1	1
   1	0	0	0
   1	0	1	1
   1	1	0	1
   1	1	1	1

   1. [3 points] A non-minimized sum of products
   2. [3 points] A non-minimized product of sums
   3. [3 points] A non-minimized circuit representing the sum of products.

5. [10 points] Simplify Σ_m(0,5,6,7,8,13,15) using a Karnaugh map. Make sure to provide the final function.
   
6. [10 points] Simplify Σ_m(1,3,5,6,7) using the Quine-McCluskey algorithm. Show all steps as performed in class. Make sure to provide the final function.