Computer architecture and organisation by Hayes John P. (John Patrick) 1944-

Author:Hayes, John P. (John Patrick), 1944-
Language: eng
Format: epub
ISBN: 0071004793
Publisher: Boston : McGraw
Published: 1998-10-18T16:00:00+00:00

Multiplicand Y 10101010

Multiplier X 11001110

0

100

P0 0000000010101100

Add -2Y to A

P2 00000000000000

2

111

Add 0 to A

P4 111110101010

4

001

Add+KtoA

P6 0001010110

6

110

Add -Y to A

P 0001000011001100

= Pu+P2 + P4 + Pb

Figure 4.64

Illustration of the modified (radix-4) Booth method of multiplication.

298 the sequential division circuit of Figure 4.23 to introduce an overflow detector using as

little extra logic as possible?

SECTION 4.5Problems

4.19. Suppose the restoring array divider of Figure 4.27 has the integer operands D = 100110and V- 101. Determine the results Q and /?, as well'as the vertical output signals gen-erated by every D cell when the array computes D/V.

4.20. Consider the divider array of Figure 4.27 that is designed to handle a word size of n =3 with a double-length (6 bit) dividend D. (a) Why are there four rows of D cells insteadof three? (b) Suppose that dividends are restricted to 3 bits instead of 6. Which cellscan then be deleted from the array?

4.21. Figure 4.65 shows a gate-level logic diagram for the 74181 ALU/function generator.The inputs have been assigned the names used in Figure 4.30, but the eight outputs areabstractly labeled/, :/g. Deduce (without using any outside sources) the correspondencebetween the output signal names in the two figures; that is, identify all the outputs inFigure 4.65 and explain your reasoning.

4.22. (a) What arithmetic and logic functions are computed by the 74181 ALU when 5 =53525,50 = 1100? (b) A useful logic operation of the 74181 is the EXCLUSIVE-ORfunction A © B. What values should 5, M, and cjn have in this case? Briefly explain yourreasoning.

4.23. The 74181 ALU is designed for use as a 4-bit magnitude comparator. For this purposeit must be set to its arithmetic subtract mode (M = 1, S = 0110) with cjn = 1. The rela-tions between the magnitudes of A and B can then be determined from the combinedvalues of the two outputs (A = B) and cout. Identify the specific output values that indi-cate each of the following: A = B, A < B, A < B, A > B, and A > B.

4.24. Show how to connect four copies of the 74181 to form a 16-bit ALU with carry looka-head across all stages.

4.25. Design a register file in the style of Figure 4.33 that stores eight 32-bit numbers andhas one read port A and one write port B.

4.26. Suppose the register file RF16 of Figure 4.33 is to be built out of four identical 4-bitslices denoted RF4. (a) Give a register-level diagram showing the internal structure ofRF4. (b) Show how four copies of RF4 are interconnected to form RF16.

4.27. Design a 16-bit bit-sliced ALU using four copies of the AMD 2901 4-bit slice. Usecarry lookahead and use NAND gates to design the necessary carry-generation logic.Give a block diagram of your design and give a set of Boolean equations that specifythe carry-lookahead function.

4.28. Suppose the 1601 ALU of Figure 4.39 operating at a clock frequency of 20 MHz isused to build an ALU intended to execute a long sequence of 80-bit additions. What isthe maximum throughput in operations per second

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