Digital Technology

Outline Week 1: Logic Gates, Boolean Algebra and Intro to HDL Week 2: Multi-level Gate Networks and Combinational Circuits Week 3: Propagation Delays and Hazards Week 4: Flips-Flops and Sequential Circuits Week 5: FSM and Revision Week 6 Test

Some Details First test: First assignment submission: First week after mid-semester First assignment submission: Friday 30 April Lecture notes are available on Moodle

Lecture Outline Logic and Logic Gates Boolean identities Truth tables Algebraic expressions Boolean identities Boolean algebra

Positive and Negative Logic If the signal that activates the circuit (the “1” state) has a voltage level that is more positive than the 0 state, then the logic polarity is considered to be POSITIVE If the signal that activates the circuit (the “1” state) has a voltage level that is more negative than the 0 state, then the logic polarity is considered to be NEGATIVE

Examples of Logic Polarity Positive logic Active signal Compliment TRUE FALSE 1 HIGH: +5 volts LOW: 0 volts Negative logic HIGH: 0 volts LOW: -5 volts

A Simple Circuit A X 1 (input) (output)

NOT Gate (Inverter) A X 1

AND Gate A B X 1

OR Gate A B X 1

NAND Gate A B X 1

NOR Gate A B X 1

XOR Gate (eXclusive OR) B X 1

XNOR Gate A B X 1

Boolean Algebra 1854 George Boole introduced a systematic approach to logic Hence Boolean Algebra 1938 C.E. Shannon introduced a two-valued Boolean algebra called switching algebra Bistable electrical circuits can expressed using this algebra

Null Law (AND) A B X 1

Null Law (OR) A B X 1

Identity Law (AND) A B X 1

Identity Law (OR) A B X 1

Idempotent Law (AND) A B X 1

Idempotent Law (OR) A B X 1

Inverse Law (AND) A B X 1

Inverse Law (OR) A B X 1

Commutative Law

Associative Law (AND) Note: same for the OR form

Distributive Law

Absorption Law

DeMorgan’s Law Change the sign (AND to OR, OR to AND) Invert the individual terms Invert the whole expression (tidy up any multiple inversions)

DeMorgans Law (hints) Use it: when you need to change the logical operation (product-of-sums for example) to get rid of any nasty inversions