An instruction pipeline has five stages where each stage takes $$2$$ nanoseconds and all instructions use all five stages. Branch instructions are not overlapped, i.e., the instruction after the branch is not fetched till the branch instruction is completed. Under ideal conditions.

(a) Calculate the average instruction execution time assuming that $$20$$% of all instruction executed are branch instructions. Ignore the fact that some branch instructions may be conditional.

(b) If a branch instruction is a conditional branch instruction, the branch need not be taken. If the branch is not taken, the following instructions can be overlapped. When $$80$$% of all branch instructions are conditional branch instructions, and $$50$$% of the conditional branch instructions are such that the branch is taken, calculate the average instruction execution time.

The most appropriate matching for the following pairs
$$X:$$ Indirect addressing
$$Y:$$ Immediate addressing
$$Z:$$ Auto decrement addressing is

$$1:$$ Loops
$$2:$$ Pointers
$$3.$$ Constants

A graphics card has on board memory of $$1$$ $$MB.$$ Which of the following modes can the card not support?

Consider the following nested representation of binary trees: (X Y Z) indicates Y and Z are the left and right sub stress, respectively, of node X. Note that Y and Z may be NULL, or further nested. Which of the following represents a valid binary tree?