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Computer Arithmetic Summary

Computer Arithmetic Summary. The wheel is come full circle. Use and Distribution Notice. Possession of any of these files implies understanding and agreement to this policy.

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Computer Arithmetic Summary

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  1. Computer Arithmetic Summary The wheel is come full circle.

  2. Use and Distribution Notice • Possession of any of these files implies understanding and agreement to this policy. • The slides are provided for the use of students enrolled in Jeff Six's Computer Architecture class (CMSC 411) at the University of Maryland Baltimore County. They are the creation of Mr. Six and he reserves all rights as to the slides. These slides are not to be modified or redistributed in any way. All of these slides may only be used by students for the purpose of reviewing the material covered in lecture. Any other use, including but not limited to, the modification of any slides or the sale of any slides or material, in whole or in part, is expressly prohibited. • Most of the material in these slides, including the examples, is derived from Computer Organization and Design, Second Edition. Credit is hereby given to the authors of this textbook for much of the content. This content is used here for the purpose of presenting this material in CMSC 411, which uses this textbook.

  3. Summary • We have now talked about integers… • signed versus unsigned • overflow conditions • addition, subtraction, multiplication, division operations • logical operations • We have talked about floating point numbers… • representations • overflow and underflow conditions • tradeoffs (no matter how you design it, everything is an approximation with FP numbers) • FP addition and multiplication algorithms • various hardware support for FP

  4. Bits, Bits, and More Bits • The most important thing to take away from this section is bit patterns have no inherent meaning! • The same set of 32 bits could be many things… • a signed integer • an unsigned integer • a floating point number (single or half of a double) • a set of bits, each with its own meaning • a machine instruction • many more things! • It is the instruction that operates on a word that determines the bits’ meaning. This is a consequence of the stored-program model.

  5. Standards and Tradeoffs • The standards we have discussed (notable IEEE 754) is one way of doing floating point arithmetic on computers. • Even though this is the standard used by all modern computers, there is nothing that would prevent you from designing a computer that used a completely different form of working with floating point values. • Like everything else in computer design, arithmetic and hardware support for it is a balance between cost and features (there are tradeoffs everywhere!).

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