Midterm Exam Review CS 2420 :: Fall 2016 Molly O'Neil
Midterm Exam Thursday, October 20 In class, pencil & paper exam Closed book, closed notes, no cell phones or calculators, clean desk 20% of your final grade 80 minutes to complete the exam Please bring a pencil and eraser! All writing will be done on exam paper that I'll hand out 2
Exam Format 100 points total 5 pages, each with 4 problems = 20 problems total (~4 minutes per) Each problem is worth 5 points -- regardless of difficulty Consider working on easy problems first! You must show work/reasoning to receive any credit! Each page has a different topic: 1: Numbers 2: Boolean Algebra & Gates 3: Canonical Forms / NAND Circuits 4: K-Maps & Minimization 5: CL Circuit Design / Structured Design Types of questions: Exercises very similar to homework problems......plus short-answer concept questions 3
Content Slides from lecture: Introduction, Motivation, & Background Numbers, Coding, & Arithmetic Binary Logic & Gates Boolean Algebra & Functions K-Maps & Minimization Combinational Circuits & Structured Logic Design Lecture slides: http://cs.txstate.edu/~mo1162/cs2420/schedule.html All homeworks (HW 1, HW 2, HW 3) NO HDLs/SystemVerilog! Nothing from lab! 4
Things You Should Know How to Do... (I) A. Numbers (1) Convert a hex # to octal via binary (2) Convert an octal # to hex via binary (3) Convert a fractional decimal # to binary (4) Convert a fractional binary, octal, or hex # to decimal (5) Describe 2's complement vs. 1's complement vs. signedmagnitude and their relative advantages/disadvantages (6) Represent a negative decimal # in 2's complement (7) Perform subtration on decimal #s using 2's complement encoding and binary arithmetic (must show work, including carries!) (8) Represent a decimal # in BCD 5
Things You Should Know How to Do... (II) B. Gates (1) Explain the operation (and/or draw a truth table) and know the symbols for AND, OR, NOT, NAND, NOR, XOR, and XNOR gates (2) Explain why NAND and NOR gates are universal (3) Draw a logic diagram from a Boolean expression (4) Construct a Boolean expression from a logic diagram C. Boolean Algebra (1) Construct a truth table from a Boolean expression (2) Demonstrate the validity of an identity via a truth table (3) Reduce a Boolean expression to a given # of literals using theorems & postulates (not K-Maps!) (4) Provide the complement of a function using DeMorgan's theorem 6
Things You Should Know How to Do... (III) D. Canonical Forms (1) Via a truth table, express a function in canonical SOP form (as an expression) or as a sum of minterms (2) Via a truth table, express a function in canonical POS form (as an expression) or as a product of maxterms (3) Convert between maxterm/minterm #s and Boolean expressions (4) Express a Boolean function in canonical SOP or POS form working directly from the expression, not via truth table (5) Describe the relationship between the minterms and maxterms of a function E. NAND Circuits (1) Use bubble-pushing/demorgan's equivalencies to express a function using only NAND gates 7
Things You Should Know How to Do... (IV) F. K-Maps (1) Simplify a 3-variable function (given as an expression, truth table, or sum-of-minterms) to a minimal 2-level SOP using a K-Map (2) Simplify a 4-variable function (given as an expression, truth table, or sum-of-minterms) to a minimal 2-level SOP using a K-Map (3) Using a K-Map, simplify a Boolean expression with don't-care conditions (4) Identify prime implicants and essential prime implicants in a K- Map G. Minimization (1) Further simplify a reduced 2-level SOP expression (derived from a K-Map) by identifying common factors (2) Further simplify a reduced 2-level SOP expression (derived form a K-Map) by identifying XOR/XNOR patterns 8
Things You Should Know How to Do... (V) H. Combinational Logic Circuit Design (1) Given a description of a CL circuit's operation, draw a truth table for the function(s) (2) Use K-Maps to derive a simplified implementation of a multi-output combinational circuit (3) Identify a static timing hazard in a K-map and give a fix (4) Draw a waveform demonstrating the output values of a circuit over time, given a series of input changes I. Structured Logic Design (1) Use a mux to implement a Boolean function by using some of its input variables as mux selects and placing factored functions of the remaining variables on the mux inputs (2) Implement a canonical SOP expression using a decoder (3) Describe the operation of a multiplexor and demultiplexor (4) Understand and describe the internals of a half-adder 9
How to Prepare Review the slides Understand all the concepts Quiz yourself Review the homework solutions (on TRACS) Re-do the homeworks (without consulting any notes) And re-check your answers against the solutions Email me with questions that come up while you study Sleep! Eat breakfast! 10