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ECEN 3733 | Digital Circuit Design | Class Notes, Lecture notes of Digital Systems Design

Youngstown State University (YSU)Digital Systems Design

ECEN 3733 - Digital Circuit Design Class Notes

Typology: Lecture notes

2016/2017

Uploaded on 10/19/2017

pkmaurer
pkmaurer 🇺🇸

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Class note #1
By Dr. Frank X. Li
ECEN 3734 Computer Design
•Understand Basic switching theory & Familiar with
–Number Systems: Binary, Decimal, etc.
–Linear Algebra: basic operations of Boolean
algebra
–Algebraic Simplifications
•Karnaugh Maps
•Quine-McClusky Method
•Be able to design and model Multi-Level Gate
circuits
–NAND, NOR Gates
–Multiplexers, Decoders, etc.
–Programmable Logic Devices, ROM, RAM,
FPGA.
Class Objectives
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Download ECEN 3733 | Digital Circuit Design | Class Notes and more Lecture notes Digital Systems Design in PDF only on Docsity!

Class note

By Dr. Frank X. Li

ECEN 3734 Computer Design

  • Understand Basic switching theory & Familiar with
    • Number Systems: Binary, Decimal, etc.
    • Linear Algebra: basic operations of Boolean algebra
    • Algebraic Simplifications
      • Karnaugh Maps
      • Quine-McClusky Method
  • Be able to design and model Multi-Level Gate circuits - NAND, NOR Gates - Multiplexers, Decoders, etc. - Programmable Logic Devices, ROM, RAM, FPGA. Class Objectives
  • Be able to design and model sequential

circuits

  • Latches and Flip-flops
  • Registers and Counters
  • Very high speed Hardware Description

Language

  • Object oriented type programming language
  • Describe the behavior and structure of
    • Simply Gates
    • Full Adder, etc.
  • Sequential Circuits
  • Finite State Machines
  • State Table & Graph Class Objectives Digital Systems

Arithmetical Algorithms Addition How about subtraction binary numbers

  • The binary number system makes some

operations especially simple and efficient

under certain representations.

  • Two such representations are
    • 1’s complement
    • 2’s complement
  • Each makes subtraction much simpler.
  • Each has disadvantage that number

length is pre-determined.

1’s Complement

  • Fix k bits. ( k = 8 for bytes)
  • Represent numbers with | x | < 2 k -^1
  • Left-most bit tells the sign
    • 0 – positive (so positive no.’s as usual)
    • 1 – negative (but other bits change too!)
  • Positive numbers the same as standard binary expansion
  • Negative numbers gotten by taking the Boolean complements 1’s Complement example

k = 8:

00010010 represents 18 11101101 represents - 18 Notice: when add these representations as usual get 11111111, i.e. negative 00000000 or - 0 = 0.

Observe: adding numbers with mixed sign works

the same as adding positive numbers

Note: 0 not unique

Binary Subtraction, 2’s Complement Binary Code

  • For computers to process our letters,

digits, punctuation marks, etc, we need a

binary code for each such “character”.

  • American Standard Code for Information

Interchange (ASCII) provides these codes.

  • Standard 8 bit bytes and 16 bit words are

not integer multiples of 3 bits but are

integer multiples of 4 bits – favoring use of

Hex!

ASCII Code