1. Erik Jonsson School of Engineering and Computer Science FEARLESS Engineeringwww.utdallas.edu/~pervin EE/CE 2310 – HON/002 Introduction to Digital Systems http://www.utdallas.edu/~pervin Thursday: (P) Chapters 9 & 10 Tuesday 4-10-12

2. EXAMINATION II: 5 A PRIL 2012 (P) 5 Functions and Stacks 6 File and Character IO 7 Recursion (T) 8 Arithmetic 9 Flip-Flops (1-6) 10 Counters (1-4) 11 Shifts (1-3) From notes, also: Timing Diagrams

10. Floating-Point Numbers IEEE-754-2008 Standard Our text only refers to the very similar IEEE-754-1985 Standard This material will be on the final as an important subject.

11. Normalized Numbers: Decisions: Base, Sign, Exponent, Mantissa

12. Decisions: (32-bit words) Base: 2 Sign: Bit 31 (0 = pos, 1 = neg) Exponent: 8 bits (biased by -127 ; not 2’s complement or other) Mantissa: 23 remaining bits (with 1. understood to give 24 bit accuracy)

13. Decisions: (64-bit words) “double” Base: 2 Sign: Bit 31 of the first word (0 = pos, 1 = neg) Exponent: 11 bits (biased by -1023 ; not 2’s complement or other) Mantissa: 20+32=52 remaining bits (with 1. understood to give 33 bit accuracy)

14. Decisions: (128-bit words) “quad” Base: 2 Sign: Bit 31 of the first word (0 = pos, 1 = neg) Exponent: 15 bits (biased by -16383 ; not 2’s complement or other) Mantissa: 112 remaining bits (with 1. understood to give 33 bit accuracy)

16. Special Cases: Zero Denormalized numbers Positive and negative infinity NaN Some other decisions:

17. We cannot store the important number 1/10 exactly in a binary computer!

18. 9.3 Extremes

19. Small Numbers

20. Large Numbers

21. 9.5 Accuracy

22. Catastrophic Cancellation

23. Hilbert Matrices Check MATLAB!

24. Floating-point Registers

26. Instructions Swcz $, $

28. geoseries.s