Chapter 2: Fundamentals of Digital Electronics Dr Mohamed Menacer Taibah University

Abstract The basics of Boolean algebra will be introduced, starting from simple combinational logic functions and basic sequential logic circuits such as latches and flip-flops. Transistor basics will be reviewed and circuits introduced that demonstrate implementations of the basic logic elements in TTL/CMOS technology. Based on these fundamentals, more complex logic structures such as decoders, adders, registers, and memories will constructed and their performance analyzed. The logic functions used as the architectural basis for programmable devices used in spaceborne electronics will be examined and analyzed.

Outline Introduction Basic Logic Hardware (Transistors, Gates) Combinational Logic Sequential Logic Module Design in Programmable Devices

Basic Digital Logic

Logic Values For binary hardware Either a ‘1’ or a ‘0’ Either a ‘1’ or a ‘0’ “Most of the time” “Most of the time” Other types of hardware can be have more than two values Simulation can use a multi-value logic system VHDL Std_Logic uses a nine-valued logic VHDL Std_Logic uses a nine-valued logic

Binary Hardware Logic Values Logic ‘1’ Logic ‘0’ Undefined value

TTL Logic Levels Logic ‘1’ threshold - V IH  2.0 V Logic ‘0’ threshold - V IL  0.8 V Undefined 0.8 V < v < 2.0 V

TTL Logic Levels Examples of Undefined Values Floating signals may take on illegal values What happens during a signal transition? 0.8V 2.0V Logic ‘0’ Undefined Logic ‘1’

Logic Values and Basic Functions

Logic Values Levels '0' or '1' '0' or '1'Pulses Presence or absence of pulses Presence or absence of pulses Pulse widths Pulse widths Number of pulses Number of pulses Zero crossings 5 Digital Waveform Time Voltage (V) 1 0 1

Switching Algebra Two-valued variable from {0,1} Two binary operations AND ( ) AND ( ) OR ( + ) OR ( + ) One unary operation NOT ( ) NOT ( )

Unary Operation - NOT A Y NOT Operator Truth Table AB The NOT gate reverses the input

Binary Operation - AND A B Y AND means that both conditions must be true in order for the conclusion to be true A Inputs B Output

Binary Operation - [Inclusive] OR A B Y Another basic operator is the OR OR works such that the output is true, if either of the two inputs is true

Digital XOR We can build an electrical device that performs the logical XOR operation on voltage equivalents of logic values An XOR gate has the electrical schematic: XOR Operator Truth Table 000 ABOutput A Inputs Output B

All digital computers are built using only three gate types: AND, OR, and NOT

Transistors

Transistor Definitions MOS - Metal Oxide Semiconductor FET - Field Effect Transistor BJT - Bipolar Junction Transistor

Transistor npn bipolar transistor collector base emitter

NAND NOR NOT