1 / 13

Data Representation – Chapter 3

Data Representation – Chapter 3. Section 3-1. Terminology. “Digital” Discrete, well defined values/steps Opposite of analog Analogy: digital is to analog as int is to double “Binary” A system consisting of two states on/off, true/false, yes/no, high/low, 0/1 Basis for modern computers.

reid
Download Presentation

Data Representation – Chapter 3

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Data Representation – Chapter 3 Section 3-1

  2. Terminology • “Digital” • Discrete, well defined values/steps • Opposite of analog • Analogy: digital is to analog as int is to double • “Binary” • A system consisting of two states • on/off, true/false, yes/no, high/low, 0/1 • Basis for modern computers

  3. Terminology • “Bit” • Binary-digit • Smallest unit of storage in modern computers

  4. Data Representation • 1000001 – what does this “mean”? • one million, one • sixteen million, seven hundred seventy seven thousand, two hundred, seventeen • two hundred sixty two thousand, one hundred forty five • sixty five • “A” • AJMP assembly language instruction

  5. Data Representation • 1000001 • Decimal number • Hexadecimal number • Octal number • Binary number • ASCII character • 8051 machine instruction

  6. Number Systems • A number system is defined by its base or radix • The number of unique digits used in the system • Digits range in value from 0 to radix-1 • Larger values are created by stringing together digits • Resultant value is defined by • d: digit, b: base, i: position with 0 being the first position to the left of the “base point”, increasing to the left, decreasing to the right

  7. Number Systems • Binary is convenient/efficient for use in a computer… • Electronic circuits can be easily designed to deal with two distinct levels • e.g. TTL 0-volts and 5-volts • … but extremely inconvenient for human consumption • Humans were designed to work with ten distinct levels • e.g. fingers • We’ll concentrate on decimal, hexadecimal, octal, and binary

  8. Conversion • Base b to decimal, b = 2 (binary) • Decimal to base b • Integer divide value by b • Output remainder • Repeat on quotient • Until quotient is zero

  9. Conversion • Binary to octal • Separate binary number into groups of 3 binary digits padding the left with 0’s if necessary • Convert groups to decimal digits 10012 -> 001001 -> 118

  10. Conversion • Binary to hexadecimal • Separate binary number into groups of 4 binary digits padding the left with 0’s if necessary • Convert groups to decimal digits 10102 -> 1010 -> 1016(?) • Not exactly • 1010—1510 -> A16—F16 • i.e. 0123456789ABCDEF

  11. Conversion • Octal to hexadecimal and hexadecimal to octal • Convert to binary then to the target radix using previous methods

  12. Conversion • Octal and hexadecimal are useful when working closely with the architecture • Designing circuits • Designing device interfaces • Writing assembly language programs • In such situations one is generally concerned with bit patterns rather than the decimal value • The conversions can be done in your head

  13. Homework – chapter 3 • 3-1, 3-2, 3-3, 3-4, 3-5, 3-6, 3-7, 3-8 • Due Thursday • Will discuss in class

More Related