The von Neumann Model

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Bits, Data types, and Operations Chapter 2
COMP 2610
Dr. James Money COMP 2610
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Floating Point Data Type

• Most ISAs have a data type called float, which is
  32 bits arranged as follows
• 1 bit for sign
• 8 bits for range of exponent
• 23 bits for the precision or fraction
• This is called the IEEE Standard for Floating
  Point Arithmetic

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Floating Point Data Type
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Floating Point Data Type

• Recall the bits in the fractional part are of the
  form
• 1.b-1b-2b-j
• The corresponding decimal number is
• 1x20 b-1x2-1b-2x2-2 b-j 2-j

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Floating Point Data Type

• If the exponent00000000, then we can represent
  tiny numbers.
• In this case, we assume the leading digit is zero
  and not 1 and exp-126. That is, it is of the
  form
• -1s 0.fraction x 2-126

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Floating Point Data Type

• Consider the floating point value
• 0 00000000 0000100000000000000000
• This is
• 2-5 x 2-126 2-131

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Floating Point Data Type

• Interpret the floating point values
• 0 11111110 1111111111111111111111
• 1 00001101 0111000000000000000000
• 1 00000000 0000000000001000000000

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ASCII Codes

• Another standard of representation is one for
  transferring character codes
• This is an eight bit code referred to ASCII
• ASCII stands for American Standard Code for
  Information Exchange
• It simplifies the interface between I/O devices
  among companies

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ASCII Codes

• Each key on a keyboard is identified by a unique
  ASCII code
• The digit 3 is (00110011)2 (41)10, digit 3 is
  (00110010)2 (40)10
• The letter e is (01100101)2 and carriage return
  is (00001101)2

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ASCII Codes

• The list of codes are at the back of the book for
  all 256 ASCII codes
• Some codes are associate with multiple keys, such
  as e and E

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Hexadecimal Notation

• One form that is common for reading values on the
  computer is called hexadecimal notation
• Hexadecimal notation is the base 16
  representation of the number

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Hexadecimal Notation

• We use 0-9 for the same numbers in hexadecimal
• What about 10-15?
• We use the letters A-F

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Hexadecimal Notation

• A 10
• B 11
• C 12
• D 13
• E 14
• F - 15

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Hexadecimal Notation

• Consider the binary string
• 0011110101101110
• This can be broken into groups of 4 bits
• 0011 1101 0110 1110
• Now, recall that the range of 4 bits is 0 -15,
  just like hexadecimal notation

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Hexadecimal Notation

• Hence, the numbers represent
• We typically prefix this by x or 0x to indicate
  hexadecimal form
• So our binary number is 0x3D6E

0011 1101 0110 1110
3 13 6 14
3 D 6 E
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Hexadecimal Notation

• What is the number 0x5A6C in binary form?
• Thus, (5A6C)16 (0101 1010 0110 1100)2

5 A 6 C
5 10 6 12
0101 1010 0110 1100