Digital Logic “102” 26 August 2013 Mark Schmalz

CDA 3101 Fall 2013Introduction to Computer Organization Digital Logic “102” 26 August 2013 Mark Schmalz http://www.cise.ufl.edu/~mssz/CompOrg/Top-Level.html

Overview • Review of gates and truth tables • Boolean algebra • Complex logic circuits • Combinational logic systems • Clocking • Memory elements

Transistors Symbol Functional Behavior NOT gate (Inverter)

Gate Symbol Truth Table NOT Gate NAND Gate

AND, OR, NOR Gates NOR

Boolean Algebra • Basic operators: OR (sum), AND (product), NOT • Boolean laws:

Circuit Equivalence

M = ABC + ABC + ABC + ABC The Majority Function M = f (A, B, C)

M = ABC + ABC + ABC + ABC The Majority Function (cont’d) M = f (A, B, C) Step 1. Build truth table for logic function f. Step 2. Write logic equation in SOP form. 3b 1 1 0 3a Step 3.a) Build SOP circuit using minterms (M=1); b) OR minterms

Combinatorial Logic • Many inputs and many outputs • Outputs are uniquely determined by inputs • Absence of memory elements • Basic combinatorial circuits • Multiplexers • Demultiplexers • Decoders • Comparators

Multiplexer 2n data inputs 1 data output n control inputs

Decoder n data inputs 2n data outputs 3-to-8 decoder

Comparator

Two-Level Logic PLA 12 inputs 6 outputs x

Clocks Clock period

Edge-Triggered Clocking State Element 1 State Element 2 Combinational logic State Element Combinational logic

NOR SR Latch State 0 State 1 S - set Inputs Outputs: Q and Q R - reset

Clocked SR Latch

Clocked D Latch D C Q

D flip-flop D D Q D Q Q D latch D latch Q C C Q C Setup time D hold time C Q

 Conclusions • Digital logic – lowest level of CDA3101 worldview • Digital logic circuits • Made from building blocks (AND,OR,NOT,…) • Simple or Complex, Combinatorial • Synchronous (clocked) or Asynchronous • Know rules for Boolean Algebra Enjoy your week!!

Digital Logic “102” 26 August 2013 Mark Schmalz