| Algorithms and Data Structures in C++ by Alan Parker CRC Press, CRC Press LLC ISBN: 0849371716 Pub Date: 08/01/93 |
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4.6 Problems
- (4.1) Modify Code List 4.1 to simulate 16, 32, and 64-bit 2s complement addition. Add a procedure to detect for overflow and indicate via output when overflow has occurred.
- (4.2) Modify Code List 4.5 to simulate a CLA adder with 3 sections each with 3 groups each with 8 1-bit adders.
- (4.3) Write a C++ program to simulate restoring division. Your program should support n bit inputs. Use the overload operators to perform addition and subtraction of each of the inputs.
- (4.4) Modify the Code List 4.13 to support n bit inputs. Use a similar register structure as the example in Figure 4.14.
- (4.5) First by example, then by proof, demonstrate the technique of shifting over 1s and 0s in non-restoring division.
- (4.6) Write a C++ program to simulate modify Code List 4.15 to shift over 1s and 0s.
- (4.7) Derive the conditions for overflow in fixed point division.
- (4.8) Add all the common logical functions to Code List 4.7.
- (4.9) Rewrite Code List 4.7 to simulate a JK Flip-Flop.
- (4.10) Calculate the average number of operations required in the Booth algorithm for 2s complement multiplication. How does this compare to the shift-add technique?
- (4.11) Modify Code List 4.7 to simulate Carry Lookahead Addition at the gate level for an 8-bit module.
- (4.12) [Moderately Difficult] Modify Code List 4.13 to output, to a PostScript file, the timing diagram for the circuit which is simulated. Make rational assumptions about the desired interface. Use the program to generate a PostScript file for the timing diagram in Figure 4.12.
- (4.13) Graphically illustrate Newtons method described in Eq. 4.37.
- (4.14) Theoretically demonstrate that the gcd function in Code List 4.21 does in fact return the greatest common divisor of the inputs x and y.
- (4.15) [Uniqueness] Show that if a residue number system is defined with moduli
and A and B are integers such that
and if
with
then
- (4.16) If mi and mj are integers satisfying
with
and
prove that if
then
- (4.17) Prove that Eq. 4.59 is true.
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