1. Lecture 24: 12/3/2002CS170 Fall 20021 CS170 Computer Organization and Architecture I Ayman Abdel-Hamid Department of Computer Science Old Dominion University Lecture 24: 12/3/2002

2. CS170 Fall 20022 Outline Appendix B Example on Memory Elements More on Combinatorial Logic

3. Lecture 24: 12/3/2002CS170 Fall 20023 Example on Memory Elements Problem B.23 (See handout) Design a 3-bit counter using D latches and gates As exercise, try to solve B.24

4. Lecture 24: 12/3/2002CS170 Fall 20024 More on Combinatorial Logic 1/4 ROMread-only memory A set of locations that can be read The contents of these locations are fixed, usually at the time the ROM is created PROM, EPROM A set of input address lines (just as a PLA), say M of these.; there are 2 M addresses and these point to 2 M distinct words A set of output lines (just as a PLA) say N, giving a word of N bits Contrast a ROM and a PLA

5. Lecture 24: 12/3/2002CS170 Fall 20025 More on Combinatorial Logic 2/4 Don’t Cares Situations where we do not care what the value of some output is, either because another output is TRUE or because a subset of input combinations determines the values of the outputs. Two types of Don’t cares Output: don’t care about the value of an output for some input combination (appear as X in the output portion of truth table) Input: Output depends on only some of the inputs (appear as X in the input portion of the truth table)

6. Lecture 24: 12/3/2002CS170 Fall 20026 More on Combinatorial Logic 3/4 InputsOutputs ABCDEF 000000 001101 010011 011110 100111 101110 110110 111111 If A or C is true, output D is true, whatever the value of B If A or B is true, output E is true, whatever value of C Output F is true if exactly one of the inputs is true. We don’t care about the value of F, whenever D and E are both true. Truth table without don’t cares InputsOutputs ABCDEF 000000 001101 010011 01111X 10011X 10111X 11011X 11111X Truth table with output don’t cares InputsOutputs ABCDEF 000000 001101 010011 X1111X 1XX11X Simplified truth table Input/Output don’t cares

7. Lecture 24: 12/3/2002CS170 Fall 20027 More on Combinatorial Logic 4/4 If A or C is true, output D is true, whatever the value of B If A or B is true, output E is true, whatever value of C Output F is true if exactly one of the inputs is true. We don’t care about the value of F, whenever D and E are both true. Truth table without don’t cares InputsOutputs ABCDEF 000000 001101 010011 01111X 10011X 10111X 11011X 11111X Truth table with output don’t cares InputsOutputs ABCDEF 000000 001101 010011 X1111X 1XX11X Simplified truth table Input/Output don’t cares How many product terms for original truth table? How many product terms for simplified truth table?