Overview of course content • Specification of digital functions and system • • • • Digital building blocks • • • • Combinatorial systems • • • • Digital Arithmetic • • • • Synchronous systems and state machines • Asynchronous systems and state machines • A little larger digital systems - the CPU and • • • computers VHDL is not significantly included - because it will need a complete course for itself. William Sandqvist william@kth.se
Digital Design IE1204 Digital Design Everywhere! William Sandqvist william@kth.se
40-100 microprocessors in a car! • Ignition system • Emission control system • Anti-lock brakes • Dashboard display • Entertainment system • Navigation system • . . . William Sandqvist william@kth.se
The development of electronics Intel 4004 Intel Xeon 5400 ( 1971 ) ( 2008 ) 3.0 GHz 820 millions of transistors 108 KHz 2,300 transistors If there had been a corresponding development of the car speed, one would be able to drive from San Francisco to New York in about 13 seconds (Intel). William Sandqvist william@kth.se
Why is digital technology so successful? William Sandqvist william@kth.se
Simplicity, imunity of electromagnetical disturbances. • Simple mathematical model – with only 1's and 0's as values – Boolean algebra • Imunity of electromagnetical disturbances , effective implementation of the mathematical model – Transistors – Integrated circuits – Advances in semiconductor technology • Efficient design methods and tools William Sandqvist william@kth.se
Analog or Digital signals? An analog signal can assume continuous values, while a digital signal may assume only discrete Analog values (here, 0 ... 5) continuous 5 101 signal 4 100 3 011 Digital signal 2 with discrete 010 values 1 001 value 000 001 010 001 010 011 100 100 011 011 time William Sandqvist william@kth.se
Digital should be worse? But if you have enough bits and sufficiently high sampling rate , the digital signal mimics the analog signal 1011 Analog signal Digital signal (3 bits) 1001 • • Digital signal (4 bits), • • • • • • double sampling frequency 0111 0101 0011 value 0001 0011 0101 0011 0101 0111 1001 1001 0111 0111 time William Sandqvist william@kth.se
Digital technology is very insensitive to interference Voltage V DD • It is not only one voltage value Logic value 1 which is translated as ”1” or ”0”, it’s a wider voltage ranges. V 1,min • A disturbance of some mV can Undefined affect the value of an analog signal a lot, but it will not move V 0,max the value out of the digital range. Logic value 0 V SS (Gnd) William Sandqvist william@kth.se
Imunity of electromagnetical disturbances Great Analog: affection Digital: Unaffected • Digital data processing can be done insensitive of electromagnetic disturbances! William Sandqvist william@kth.se
Digital Signal Processing When possible all signal processing is done digitally today Analog-Digital Converter Digital-Analog Converter Antenna Microphone Carrier frequency Digital ADC DAC Signal processing 01101010100 1010101 10 101010 Analog signal Digital signals Modulated signal IE1204 Digital Design 11
Catching the data is still critical! 100111011101111011110 Although most of the signal processing is now done digitally and thus safe from interference, it is still critical to "catch" the data in a good way – the analog / digital conversion! Any disturbancies that accompany the data into the digital system we then will have to live with! William Sandqvist william@kth.se
Mathematical model - Boolean algebra: axioms • In Boolean algebra, there is only one (true) and 0 (false) as values • The following operations are defined: AND ( � ), OR (+), NOT (x) • The following axiom defines the Boolean algebra William Sandqvist william@kth.se
Booleska Algebra: rules Rules can be derived from axioms – many of the rules are consistent with our usual algebra! – comfortable that we can continue to use rules as has been done in primary school! – but beware! Some rules are new and different! • • • • More soon in the course ... William Sandqvist william@kth.se
The technical background When telephone exchanges were automated, Boolean algebra was used as a tool to calculate how the networks could be simplified. The switches is drawn in their unaffected state. Making contact ⋅ ⋅ ⋅ ⋅ for serial connection, Breaking contact, ”not” the ”and” -function + for parallell connection the ”or”-function William Sandqvist william@kth.se
Gates instead of switches + ”or”-gate The switches were eventually replaced by ⋅ ⋅ ⋅ ⋅ ”and”-gate "gates" made of electronic components ”not” inverter With these three basic gate types: OR AND NOT can all logical functions be performed. • • • • More soon in the course ... William Sandqvist william@kth.se
Only one single gate type! Actually it will Suffice with one single gate type, NAND , for making every other! Extreme simplification, one single gate type is enough for everything! • • • • More soon in the course ... William Sandqvist william@kth.se
CMOS NAND - gate An effective implementation of CMOS NAND gate requires only four transistors ... A N-MOS transistor. CMOS gates consume only effect when changing state. Good thing, otherwise today's computer chips would be even hotter. • • • • More soon in the course ... William Sandqvist william@kth.se
Memoryfunction? Traffic lights and elevators must "remember" your button presses. This is done by "flip- flops" or "latches" - which you can also make with NAND gates. • • • • More soon in the course ... William Sandqvist william@kth.se
See-of-Gates Because only one single type of gates is needed, you can do anything with a "sea of gates" completed with printed wires designed for its own specific function. William Sandqvist william@kth.se
See-of-Gates Because only one single type of gates is needed, you can do anything with a "sea of gates" completed with printed wires designed for its own specific function. William Sandqvist william@kth.se
William Sandqvist william@kth.se
How to design with a billion gates? A modern processor can contain a billion gates - you can not draw such a circuit diagram by hand ... We need other methods to describe such a system! William Sandqvist william@kth.se
CAD-tools • A CAD tool is a program that helps the engineer to design (eg, an integrated circuit) • CAD tools can be fully automated or interactive • CAD tools are based on algorithms that define the order of a sequence of methods to be applied William Sandqvist william@kth.se
Hardware description languages The Design is described with an entity (black box) and an architecture (the content of the box) Entity Outputsignals Inpursignals Architecture William Sandqvist william@kth.se
Design-tools Step 1 : VHDL-Description of VHDL-code the desired hardware is translated into Boolean equations Equations Step 2 : Boolean equations is translated to the available hardware Implemen- tation In the course You will try out the design tool Quartus II William Sandqvist william@kth.se
Example of VHDL-code LIBRARY ieee ; USE ieee.std_logic_1164. all ; ENTITY mux4to1 IS PORT ( w0, w1, w2, w3 : IN STD_LOGIC ; s : IN STD_LOGIC_VECTOR (1 DOWNTO 0) ; f : OUT STD_LOGIC ) ; END mux4to1 ; ARCHITECTURE Behavior OF mux4to1 IS BEGIN VHDL is a very complex WITH s SELECT language - this course can not f <= w0 WHEN "00", accommodate so much of this. w1 WHEN "01", w2 WHEN "10", Advanced level courses w3 WHEN OTHERS ; are available! END Behavior ; William Sandqvist william@kth.se
Boolean equation f = s 1 ⋅ s 0 ⋅ w 0 + s 1 ⋅ s 0 ⋅ w 1 + s 1 ⋅ s 0 ⋅ w 2 + s 1 ⋅ s 0 ⋅ w 3 • • • • More soon in the course ... William Sandqvist william@kth.se
A gate circuit that implements the function The textbook uses American symbols: AND OR NOT • • • • More soon in the course ... William Sandqvist william@kth.se
William Sandqvist william@kth.se
Technology Advances The trend is furious fast ... William Sandqvist william@kth.se
Digital hardware in a computer System Modules Gates and flip-flops Transistors William Sandqvist william@kth.se
The Designprocess In the course we are simulating a design with Model Sim William Sandqvist william@kth.se
Binary numbers Digital technology uses only two numerical symbols: 0 and 1 – Easy to implement - each value corresponds to a voltage level, e.g. 0 Volt corresponds to 0 5 Volt corresponds to 1 How can ordinary numbers be represented? William Sandqvist william@kth.se
Decimal number system In the decimal number system we have 10 different numeric symbols: 0 - 9 A decimal number is represented with a sequence of numeric symbols – The position in the sequence gives the digit its weight and is multiplied by a power of 10 (the base of the decimal system is 10) = ⋅ + ⋅ + ⋅ 2 1 0 ( 653 ) 6 10 5 10 3 10 10 William Sandqvist william@kth.se
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