Digital Logic Overview

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Contents of the individual courses in WS 2019/20

Part 1 Basics Pages
10/22/2019 Introduction; digital abstraction; information, coding (fixed/variable length); number representation; Hamming distance 1-32
10/29/2019 Boolean algebra; Huntington's axioms; DeMorgan's laws; propositional logic; switching algebra; function representations 33-60
Nov. 05, 2019 Switching functions; minterm/Maxterm representations; main theorem of switching algebra; canonical forms; KV diagrams; basic systems 61-83
Nov. 12, 2019 Evolution 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  
Nov 19, 2019 KV minimization; switching networks, combinat. Contract; design flow; example: 2x2 bit multiplier; Quine/McCluskey minimization: quine tables, coverage function, bundle minimization 116-146
11/26/2019 Pos./neg. logic; output/input tolerance; MOS-FETs, gates, inverters, pullup/pulldown networks; NAND, NOR, AND; propagation delay, hazards: stat. 0-/1-hazard, full coverage, dyn. hazards 147-175
11/26/2019 Evening Wrapup Fundamentals: 6:00 pm to 8:00 pm, HS 0425: table -> formula -> KV ->table; circuit diagram; KV minimization.  
Part 3 Switchgear  
Dec. 03, 2019 Switching circuits: 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
Dec. 10, 2019 Analysis of RS flip-flop, clocking, clocked RS flip-flop, clocked D flip-flop 201-226
12/17/2019 Timed MS-FF, state-specific functions, transition diagram; JK-FF, D-FF: characteristic equation; switch synthesis: sequence, state encoding, driving equations for FFs 227-250
12/17/2019 Evening Wrapup Switching Networks: 6:00 pm to 8:00 pm, HS 0425: KV&KV minimization; formula->circuit diagram; KValgebr. minimization; automaton design: task->transition diagram->transition table->KVmin.->equation->circuit (example: holding element); hazards.  
Vacations Christmas break  
14.01.2020 FF control: tabular Verf., case discrimination, 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; clock period construction; path optimization; data ready time; counter/counter design; registers: construction, 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 base cell, tiling 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
02/04/2020 Evening Wrapup Switching Networks: 6:00 p.m. to 8:00 p.m., HS 0425 (Topics: your questions; modulo counters if applicable, wdh. 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
Feb. 11, 2020 evening Wrapup design, etc.: 6:00 p.m. to 8:00 p.m., 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 systems 176
Elementary switching systems 195
Switching mechanism analysis 201
Memory for a binary variable 205
RS flip-flop analysis and behavior 207
Switched RS-FlipFlop 216
Switched D-FlipFlop 222
Switched pre-memory flip-flop 227
JK-FlipFlop 237
D-FlipFlop 242
Switching unit synthesis 247
Design example series adder 265
Time response in circuits 273
Path optimization 281
Special switching mechanisms: Counters 286
Register 297
Special switching networks: Arithmetic 304
Special switching networks: Design with function blocks 330
Programmable circuits: ROM, PLA, PAL 355
Field programmable devices: FPGAs 368
Exercise sheets