Data%20Representation%20

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Data Representation Chapter 3

• Section 3-1

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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

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Terminology

• Bit
• Binary-digit
• Smallest unit of storage in modern computers

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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

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Data Representation

• 1000001
• Decimal number
• Hexadecimal number
• Octal number
• Binary number
• ASCII character
• 8051 machine instruction

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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

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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
• Well concentrate on decimal, hexadecimal, octal,
  and binary

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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

Value Quotient Value / 2 Remainder Value 2
9 4 1
4 2 0
2 1 0
1 0 1
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Conversion

• Binary to octal
• Separate binary number into groups of 3 binary
  digits padding the left with 0s if necessary
• Convert groups to decimal digits
• 10012 -gt 001 001 -gt 118

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Conversion

• Binary to hexadecimal
• Separate binary number into groups of 4 binary
  digits padding the left with 0s if necessary
• Convert groups to decimal digits
• 10102 -gt 1010 -gt 1016(?)
• Not exactly
• 10101510 -gt A16F16
• i.e. 0123456789ABCDEF

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Conversion

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

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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

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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