f37-book-intarch-pres-pt3

f37-book-intarch-pres-pt3 - Part III The Arithmetic/Logic...

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Jan. 2011 Computer Architecture, The Slide 1 Part III The Arithmetic/Logic Unit
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Jan. 2011 Computer Architecture, The Slide 2 About This Presentation This presentation is intended to support the use of the textbook Computer Architecture: From Microprocessors to Supercomputers , Oxford University Press, 2005, ISBN 0-19-515455-X. It is updated regularly by the author as part of his teaching of the upper- division course ECE 154, Introduction to Computer Architecture, at the University of California, Santa Barbara. Instructors can use these slides freely in classroom teaching and for other educational purposes. Any other use is strictly prohibited. © Behrooz Parhami Edition Released Revised Revised Revised Revised First July 2003 July 2004 July 2005 Mar. 2006 Jan. 2007 Jan. 2008 Jan. 2009 Jan. 2011
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Jan. 2011 Computer Architecture, The Slide 3 III The Arithmetic/Logic Unit Topics in This Part Chapter 9 Number Representation Chapter 10 Adders and Simple ALUs Chapter 11 Multipliers and Dividers Chapter 12 Floating-Point Arithmetic Overview of computer arithmetic and ALU design: Review representation methods for signed integers Discuss algorithms & hardware for arithmetic ops Consider floating-point representation & arithmetic
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Jan. 2011 Computer Architecture, The Slide 4 Preview of Arithmetic Unit in the Data Path Fig. 13.3 Key elements of the single-cycle MicroMIPS data path. / ALU Data cache Instr cache Next addr Reg file op jta fn inst imm rs (rs) (rt) Data addr Data in 0 1 ALUSrc ALUFunc DataWrite DataRead SE RegInSrc rt rd RegDst RegWrite 32 / 16 Register input Data out Func ALUOvfl Ovfl 31 0 1 2 Next PC Incr PC (PC) Br&Jump ALU out PC 0 1 2 Instruction fetch Reg access / decode ALU operation Data access Register writeback
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Jan. 2011 Computer Architecture, The Slide 5 Computer Arithmetic as a Topic of Study Brief overview article – Encyclopedia of Info Systems , Academic Press, 2002, Vol. 3, pp. 317-333 Our textbook’s treatment of the topic falls between the extremes (4 chaps.) Graduate course ECE 252B – Text: Computer Arithmetic , Oxford U Press, 2000 (2nd ed., 2010)
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Jan. 2011 Computer Architecture, The Slide 6 9 Number Representation Arguably the most important topic in computer arithmetic: Affects system compatibility and ease of arithmetic Two’s complement, flp, and unconventional methods Topics in This Chapter 9.1 Positional Number Systems 9.2 Digit Sets and Encodings 9.3 Number-Radix Conversion 9.4 Signed Integers 9.5 Fixed-Point Numbers 9.6 Floating-Point Numbers
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Jan. 2011 Computer Architecture, The Slide 7 9.1 Positional Number Systems Representations of natural numbers {0, 1, 2, 3, …} ||||| ||||| ||||| ||||| ||||| || sticks or unary code 27 radix-10 or decimal code 11011 radix-2 or binary code XXVII Roman numerals Fixed-radix positional representation with k digits Value of a number: x = ( x k –1 x k –2 . . . x 1 x 0 ) r = Σ x i r i For example: 27 = (11011) two = (1 × 2 4 ) + (1 × 2 3 ) + (0 × 2 2 ) + (1 × 2 1 ) + (1 × 2 0 ) Number of digits for [0, P ]: k = log r ( P + 1) = log r P + 1 k –1 i =0
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Jan. 2011 Computer Architecture, The Slide 8 Unsigned Binary Integers Figure 9.1 Schematic representation of 4-bit code for integers in [0, 15].
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f37-book-intarch-pres-pt3 - Part III The Arithmetic/Logic...

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