AET 2050 - DAW Production

2. Binary Systems

Objectives:

1. Differentiate between analog and digital representations, giving advantages and disadvantages of each
2. Convert numeric values between decimal, hexadecimal, and binary number systems
3. Identify negatives values represented by signed binary and 2's complement
4. Define bit organization in bits, bytes, and words
5. Determine the quantity of unique conditions that a given binary number range can represent
6. Compare and contrast parallel and serial data transmission
7. Give examples of other data coding systems, such as floating-point or ASCII

Analog and digital representations

• What is "digital"?
• The differences between an analog representation and a digital representation
• Advantages of digital
• Disadvantages

computers and the Binary number system

Positional-value number systems

Numeric representations in a weighted or positional system

Positional number system - properties:

• The system's radix, or base
• A set of unique digits
• Representations using digits arranged in positions
• Each position has a value, or weight
• A digit's value is determined by its position
• A number of unique states represented by a given weighted number
• Adding a digit to a number will increase the available states by a factor of the radix
• The highest value represented by a given number

Examples of a positional system

Base-10

Base-5

Base-2 (binary)

Computers and Binary

• Reasons for using binary
• Methods of binary representation

Computer data can represent any and all kinds of information, from numeric quantities to text characters, to program instructions, to audio; however, regardless what the data represents, it is always binary data.

Organization of bits

Bits are organized into logical groups:

System size and numeric range

Word length and range of values in a computer

Word length and system limits

Binary transmission

Electrically, binary words are transmitted from one device to another in either parallel or serial form.

• Parallel transmission
• Serial transmission

Other codes and representations

Binary data can represent different kinds of information, not just raw numeric quantities.

Different codes are used to represent data in different applications.

Signed binary - 2's complement

Computers represent negative numbers using 2's complement - a bit pattern that, when added, gives the correct result as though subtracted.

  An example

• The MSB can be considered a sign bit
  • 0 for positive values
  • 1 for negative values.

Signed binary causes the numeric range that a given word size represents shifts.

• The number of conditions is the same
• half of the values are now negative
• the highest positive value is only half the original value of the unsigned range.

Unsigned vs signed binary

Floating-point notation

Limits of a fixed-range system:

• Many quantities are larger (or smaller) than a system's range.
• Some data require fractional representation.

Floating-point represents quantities in scientific notation

• Mantissa and exponent are stored in defined sections of the data word

• Two words extend the precision - double-precision

Advantages and disadvantages of floating point

Character codes

Binary codes are used to represent the alpha-numeric character set used for text entry, storage, and display.

ASCII

• 8-bit code encodes all letters, numeral, punctuation and control characters that make up the western alphabet.
• 8 bits allows for 256 different characters.
• an example

Unicode

• Some languages (most notably Kanji) have many more characters. A larger code is needed.
• Unicode is a universal coding system using 16 bits, allowing for 65,536 different characters.

Other Codes

• Control information, such as MIDI messages.
• Status flags, start bits, stop bits, etc.
• Data such as color properties for screen info
• Channel codes - methods of transmitting data

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