Floating Point Numbers

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Floating Point Numbers

• CS2 Lab7

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Binary Numbers

• Binary Numbers (base 2).
• 1 Byte 8 Bits

• As an unsigned integer the above would be
  3648499417 in decimal
• 1 0 0 8 16 0 .

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IEEE Floating Point Numbers

• An approximation of the rational numbers.
• Think of it as scientific notation in base 2
• (sign) (significand) 2(exponent constant bias)
• For example

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A Bit of Details

• Sign(31)
• (0? and 1? -)
• Exponent (30 - 23)
• A number between 0 and 255 inclusive
• Biased by -127
• Significand (22-0)
• Sometimes informally referred to as the mantissa

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Normalized Form

• In scientific notation we can write
• 31.410-1
• 3.14100 (Normal Form)
• 0.314101
• 0.0314102
• Floating Point Numbers
• A floating point is said to be in normal form if
  the first digit in the significand is 1
• 0.10101 ? 1.01012-1

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A Bit of Math
Sign -1
Exponent 0(20) 1(21) 0(22) 0(23) 1(24)
1(25) 0(26) 1(27) Exponent 178
(sign) (significand) 2(exponent constant
bias) (-1) (16232153 / 8388608 ) 2(178
127) (-1) (16232153 / 8388608 ) 251 4.37529 x
1015 And you thought it would be p?
Significand 1 1(2-1) 1(2-2) 1(2-3)
0(2-4) 1(2-5) Significand 16232153 /
8388608 1.9350234270095825
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Air Hockey
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Hitting the Wall
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Working With the Air Hockey Frame Work

• Based on MissileCommand Frame Work
• GameController (The Main Class)
• If you want to play the game in full screen mode
  modify the main method of this class changing
  new GameDisplay(false) ? new GameDisplay(true)
• GameLogic (What Will Modify)
• GameState (The State of The Game)
• GameDisplay (Renders The Game)