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Chapter 4 計算機算數
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Outline
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Problem: Designing MIPS ALU
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Functional Specification
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A Bit-slice ALU
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A 1-bit ALU
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A 4-bit ALU
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How about Subtraction?
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Revised Diagram
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Overflow
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Overflow Detection
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Overflow Detection Logic
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Zero Detection Logic
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Putting It Altogether (I)
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Putting It Altogether (II)
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Problems with Ripple Carry Adder
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Carry Lookahead: Theory (I)
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Carry Lookahead: Theory (II)
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Cascaded Carry Lookahead
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Carry-select Adder
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Add XOR to ALU
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Shifters
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Combinational Shifter
What comes in the MSBs? how many levels for 32-bit shifter? what if we use 4-1 Muxes ?
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Outline
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Multiplication in MIPS
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Division in MIPS
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MIPS Multiply/Divide Summary
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Unsigned Multiply
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Unisigned Multiplier (Ver. 1)
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Observations: Multiply Ver. 1
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Unisigned Multiplier (Ver. 2)
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Unisigned Multiplier (Ver. 3)
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Observations: Multiply Ver. 3
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Booth’s Algorithm: Motivation
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Booth’s Algorithm: Rationale
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Booth’s Algorithm
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Booths Example (2 x 7)
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Booths Example (2 x -3)
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Combinational Multiplier
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How Does It Work?
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Outline
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Divide: Paper & Pencil
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Divide Hardware (Version 1)
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Observations: Divide Version 1
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Divide Hardware (Version 2)
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Observations: Divide Version 2
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Divide Hardware (Version 3)
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Observations: Divide Version 3
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Outline
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Floating-Point: Motivation
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Scientific Notation: Binary
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FP Representation
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Double Precision Representation
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IEEE 754 Standard (1/4)
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IEEE 754 Standard (2/4)
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IEEE 754 Standard (3/4)
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IEEE 754 Standard (4/4)
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Example: FP to Decimal
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Continuing Example: Binary to ???
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Big Idea: Type Not Associated with Data
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Example: Decimal to FP
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Representation for 0
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Special Numbers
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Representation for +/- Infinity
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Representation for Not a Number
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Special Numbers (cont’d)
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Floating-Point Addition
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Floating-Point Multiplication
(4) set the sign of product
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MIPS Floating Point
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Rounding
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Round to Even
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Floating Point Fallacy
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Summary
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