1. S. Mandayam/ CompArch2/ECE Dept./Rowan University Computer Architecture II: Specialized 0909.444.01/02 Fall 2001 John L. Schmalzel Shreekanth Mandayam ECE Department Rowan University http://engineering.rowan.edu/~shreek/fall01/comparch2/ Lecture 2 October 31, 2001

2. S. Mandayam/ CompArch2/ECE Dept./Rowan UniversityPlan Recall: Floating Point Representation IEEE 754 Standard IA-32 Data Types Floating Point Arithmetic IEEE 754 implementation Class Discussion: Presentation Project Selection

3. S. Mandayam/ CompArch2/ECE Dept./Rowan University Recall: FP Representation Sign bit Biased Exponent Significand/Mantissa/Fraction 8 bits 23 bits Sign of Mantissa

4. S. Mandayam/ CompArch2/ECE Dept./Rowan University Floating Point: Expressible Numbers

5. S. Mandayam/ CompArch2/ECE Dept./Rowan University IEEE 754 Standard Parameter Single Precision Single Extended Double Precision Double Extended Word width (bits)32>= 4364>= 79 Exponent width (bits)8>= 1111>= 15 Exponent bias127Unspecified1023Unspecified Max exponent127>= 10231023>= 16383 Min exponent-126<= -1022-1022<= -16382 Number range (base 10)10 -38, 10 +38 Unspecified10 -308, 10 +308 Unspecified Mantissa width (bits)23>= 3152>= 63 No. of exponents254Unspecified2046Unspecified No. of fractions2 23 Unspecified2 52 Unspecified No. of values1.98 x 2 31 Unspecified1.98 x 2 63 Unspecified

6. S. Mandayam/ CompArch2/ECE Dept./Rowan University IEEE 754 Numbers and NaNs NumberSign Biased Exponent FractionValue Positive zero0000 Negative zero100-0 Plus infinity0255 (all 1s)0Infinity Minus infinity1255 (all 1s)0-Infinity Quiet NaN0 or 1255 (all 1s)neq 0NaN Signaling NaN0 or 1255 (all 1s)neq 0NaN Positive normalized nonzero00 < e < 255f2 e-127 (1.f) Negative normalized nonzero10 < e < 255f-2 e-127 (1.f) Positive denormalized00f neq 02 e-126 (0.f) Negative denormalized10f neq 0-2 e-126 (0.f)

7. S. Mandayam/ CompArch2/ECE Dept./Rowan University IA-32 Architecture: Data Types

8. S. Mandayam/ CompArch2/ECE Dept./Rowan University IA-32 Architecture: Numeric Data Types

9. S. Mandayam/ CompArch2/ECE Dept./Rowan University IA-32 Architecture: Numeric Data Types

10. S. Mandayam/ CompArch2/ECE Dept./Rowan University IA-32: Numbers and NaNs

11. S. Mandayam/ CompArch2/ECE Dept./Rowan University FP Addition/Subtraction

12. S. Mandayam/ CompArch2/ECE Dept./Rowan University FP Multiplication

13. S. Mandayam/ CompArch2/ECE Dept./Rowan University FP Division

14. S. Mandayam/ CompArch2/ECE Dept./Rowan UniversityReferences William Stallings, Computer Organization and Architecture, 5 th Edition, Prentice-Hall, 2000. ftp://ftp.prenhall.com/pub/esm/computer_s cience.s-041/stallings/Slides/COA5e- Slides/ftp://ftp.prenhall.com/pub/esm/computer_s cience.s-041/stallings/Slides/COA5e- Slides/ IA-32 Intel Architecture Software Developer’s Manual Volume 1: Basic ArchitectureIA-32 Intel Architecture Software Developer’s Manual Volume 1: Basic Architecture http://www.intel.com/home/pentium4/

15. S. Mandayam/ CompArch2/ECE Dept./Rowan UniversitySummary