Download presentation
Presentation is loading. Please wait.
Published byKelly Evans Modified over 9 years ago
1
ECE 171 Digital Circuits Chapter 6 Logic Circuits Herbert G. Mayer, PSU Status 1/16/2016 Copied with Permission from prof. Mark Faust @ PSU ECE
2
Syllabus Combinatorial Logic Circuits Truth Tables Logic Functions References
3
Lecture 6 Topics –Combinational Logic Circuits Graphic Symbols (IEEE and IEC) Switching Circuits Analyzing IC Logic Circuits Designing IC Logic Circuits Detailed Schematic Diagrams Using Equivalent Symbols 3
4
Combinational Logic Circuits Combinational Logic –Outputs depend only upon the current inputs (not previous “state”) Positive Logic –High voltage (H) represents logic 1 (“True”) –“Signal BusGrant is asserted High” Negative Logic –Low voltage (L) represents logic 1 (“True”) –“Signal BusRequest# is asserted Low” 4
5
IEEE: Institute of Electrical and Electronics Engineers IEC: International Electro- technical Commission 5
6
n.o. = normally open n.c. = normally closed 6
7
7
8
8
9
9
10
10
11
11
12
12
13
13
14
All Possible Two Variable Functions Question: How many unique functions of two variables are there? Recall earlier question… 14
15
Truth Tables B 5 B 4 B 3 B 2 B 1 B 0 F 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 1 1 0. 1 1 1 1 1 1 1 0 1 2 3. 63 2 6 = 64 Question: How many rows are there in a truth table for n variables? As many rows as unique combinations of inputs Enumerate by counting in binary 2n2n 15
16
Two Variable Functions Question: How many unique combinations of 2 n bits? Enumerate by counting in binary 2 2 n 2 64 16 B 5 B 4 B 3 B 2 B 1 B 0 F 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 1 0 0 0 0 1 1 0. 1 1 1 1 1 1 1 0 1 2 3. 63 2 6 = 64
17
All Possible Two Variable Functions Question: How many unique functions of two variables are there? B 1 B 0 F 0 0 0 0 1 1 1 0 1 1 1 0 2 2 = 4 rows 4 bits Number of unique 4 bit words = 2 4 = 16 17
18
18
19
Analyzing Logic Circuits Reference Designators (“Instances”) X + Z X X + Y (X + Y) (X + Z) 19
20
Analyzing Logic Circuits C ABAB BCBC A B + B C 20
21
Designing Logic Circuits F1 = A B C + B C + A B SOP form with 3 terms 3 input OR gate 21
22
Designing Logic Circuits F1 = A B C + B C + A B Complement already available 22
23
Some Terminology F1 = A B C + B C + A B Signal line – any “wire” to a gate input or output 23
24
Some Terminology F1 = A B C + B C + A B Net – collection of signal lines which are connected 24
25
Some Terminology F1 = A B C + B C + A B Fan-out – Number of inputs an IC output is driving Fan-out of 2 25
26
Some Terminology F1 = A B C + B C + A B Fan-in – Number of inputs to a gate Fan-in of 3 26
27
Vertical Layout Scheme – SOP Form 27
28
Vertical Layout Scheme – SOP Form 28
29
>2 Input OR Gates Not Available for all IC Technologies Solution: “Cascading” gates 29
30
Vertical Layout Scheme – POS Form F2 = (X+Y) X+Y) X+Z) 30
31
Designing Using DeMorgan Equivalents Often prefer NAND/NOR to AND/OR when using real ICs –NAND/NOR typically have more fan-in –NAND/NOR “functionally complete” –NAND/NOR usually faster than AND/OR 31
32
AND/OR forms of NAND DeMorgan’s Theorem 32
33
Summary of AND/OR forms Change OR to AND “Complement” bubbles 33
34
Equivalent Signal Lines 34
35
NAND/NAND Example 35
36
NOR/NOR Example 36
37
37
Similar presentations
© 2025 SlidePlayer.com. Inc.
All rights reserved.