(Optional: to be used if the first 33 questions are completed ahead of time)
 
 
 
 

34. Consider a binary integer:

X=x_n-1x_n-2.....x₂x₁x₀

Express the value of X in terms of the individual bits if it is (a) unsigned (b) sign-magnitude (c) One's complement (d) Two's complement

35. Design a 32-bit floating-point number system (i.e. One in which each floating point variable would be 32-bits in size). You need to ensure that it can deliver at least  8 decimal digits of accuracy and have a range of 10^-25 to 10²⁵

36. As more and more memory is squeezed into a single memory chip, the number of pins needed to address the memory on the chip must also increase. It can be inconvenient to have a very large number of pins on a chip. Devise a way (or ways) to address the 2ⁿ words of memory on a chip, using fewer than n address pins.

37. The Sun Enterprise 10000 CPUs run at 333MHz but the snooping bus only runs at 83.3MHz (i.e. The snooping communication between the shared processors, each of which has its own large cache). The Enterprise 10000 currently contains 64 CPUs so it is clear that the snooping bus can only handle a fraction of the possible load. Although Sun have provided 4 shared snoop buses, you would still expect the machine to slow down because of the speed of the snoop bus compared to the CPU speed. However the performance of the Enterprise 10000 is extremely good. Why is it not slowed down as expected?