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 Tuesday: Review for Examination II Thursday 3-29-12

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)

3. Serial-Load Shift Reg.

4. Parallel-Load Shift Reg.

5. C(n,k) = C(n-1,k) + C(n-1,k-1); 1 1 2 1 1 3 3 1 1 4 6 4 1... Pascal Triangle

6. C(n,k) = C(n-1,k) + C(n-1,k-1); 1 1 2 1 1 3 3 1 1 4 6 4 1... Order 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14...

7. P ASCAL T RIANGLE

11. Dynamic Programming

13. T IMING D IAGRAM

14. F = AC’D + BC + A’C

17. TIMING

20. EXAMINATION II: 5 April 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)

21. Floating-Point Numbers IEEE-754-2008 Standard Our text only refers to the very similar IEEE-754-1985 Standard

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

23. 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)

24. 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)

25. 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)

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

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