Overview of Digital Logic

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Contents of the individual courses in WS 2019/20

Part 1 Basics Pages
22.10.2019 Introduction; digital abstraction; information, coding (fixed/variable length); number representation; Hamming distance 1-32
29.10.2019 Boolean algebra; Huntington's axioms; DeMorgan's laws; propositional logic; switching algebra; function representations 33-60
05.11.2019 Switching functions; minterm/maxterm representation; main theorem of switching algebra; canonical forms; KV diagrams; basic systems 61-83
12.11.2019 Development theorem; assignments; don't care; simplification: summarize (ax. V, block), transform, transformation table, KV minimization; term (order); (complete) covering; definitions: (essential) prime term, implicant etc. 84-115
Part 2 Switching networks  
19.11.2019 KV minimization; switching networks, combinat. Contract; design flow; example: 2x2 bit multiplier; minimization according to Quine/McCluskey: Quine tables, covering function, bundle minimization 116-146
26.11.2019 Pos./neg. logic; output/input tolerance; MOS-FETs, gates, inverters, pull-up/pull-down networks; NAND, NOR, AND; propagation delay, hazards: stat. 0-/1-hazard, complete coverage, dyn. hazards 147-175
26.11.2019 Evening Wrapup Basics: 18:00 to 20:00, HS 0425: Table -> Formula -> KV ->Table; Circuit diagram; KV minimization  
Part 3 Switchgear  
03.12.2019 Switchgear: feedback, output and transition behavior; representation (also blackboard); Moore/Mealy distinction; description: table, state transition graph; example (synch. memory element); taxonomy; master-slave flip-flop 176-200
10.12.2019 Analysis of the RS-FlipFlop, clocking, clocked RS-FlipFlop, clocked D-FlipFlop 201-226
17.12.2019 Synchronized MS-FF, state-specific functions, transition diagram; JK-FF, D-FF: characteristic equation; switch synthesis: sequence, state coding, control equations for FFs 227-250
17.12.2019 Evening Wrapup switching networks: 18:00 to 20:00, HS 0425: KV&KV minimization; formula->circuit diagram; KValgebr. minimization; automaton design: task->transition diagram->transition table->KV-Min.->equation->circuit (example: holding element); hazards  
Vacation Christmas break  
14.01.2020 FF-Control: Tabular Verf., case differentiation, coefficient comparison (example: counter); design example: series adder 251-272
21.01.2020 Zeitverhalten: Gate delay, critical path, FFs: setup, hold and clock-to-Q times; structure of a clock period; path optimization; data ready time; counter/counter design; registers: structure, shift register, left/right shift, register file 273-303
Part 4 Complex circuits  
28.01.2020 Binary addition; two's complement; full adder, half adder, RCA: ripple carry adder; multiplication: special cases, basic structure of the basic cell, tile structure 304-329
04.02.2020 MSI-Schaltungen: Decoder, decoder switching networks (Ex. comparator), demultiplexer, multiplexer, multiplexer switching networks/MUX for function realization (3 and more variables), read memory/ROM; Programmable logic: PLA, PAL 330-366
04.02.2020 Evening Wrapup Schaltwerke: 18:00 to 20:00, HS 0425 (topics: your questions; modulo counters, if applicable, registers, codes, arithmetic)  
11.02.2020 Microprogram control unit (see additional slides); MUX as function table, LUT, FPGA (CLB, switch matrix, array structure) 367-382
11.02.2020 Evening Wrapup design etc.: 18:00 to 20:00, HS 0425: Full adder (algebraic); MUX, demux, decoder  

Table of contents of the slides

Abstraction and information 1
Codes, number representation, 2K, Hamming 9
Digital Abstraction 23
Boolean algebra 33
Switching functions 55
KV diagrams 70
Basic systems 73
Development Theorem 84
Assignments 87
Simplification of switching functions 94
Transformation of switching functions 102
Minimization with KV diagrams 105
Definitions 110
Minimization with KV diagrams 116
Switching networks 119
Example of switching network design 124
The Quine-McCluskey method 133
Implementation technology 147
Logic realization 154
Time behavior 162
Hazards 167
Switching mechanisms 176
Elementary switching mechanisms 195
Switching mechanism analysis 201
Memory for a binary variable 205
Analysis and behavior of the RS FlipFlop 207
Clocked RS-FlipFlop 216
Clocked D-FlipFlop 222
Clocked pre-memory FlipFlop 227
JK-FlipFlop 237
D-FlipFlop 242
Gearshift synthesis 247
Design example series adder 265
Time behavior in circuits 273
Path optimization 281
Special switching mechanisms: Counters 286
Registers 297
Special switching networks: Arithmetic 304
Special switching networks: Design with blocks 330
Programmable circuits: ROM, PLA, PAL 355
Field programmable devices: FPGAs 368
Exercise sheets