| HOMEWORK #3 |
CSE 410 Fall 98 |
Due: Wednesday October 21, in class
1. [PH] Exercise 3.19 (pp.201-203)
2. Assume a machine with 2-address instructions and several general
purpose registers. Each register and memory cell has 32 bits, numbered
from 0 (least significant) to 31 (most significant). The machine has a
move x, y
instruction, where x and y could refer to either registers or main
memory locations, as well as a standard set of logical and shift
instructions. Operands for these could refer to registers or memory, or
could be constants or "immediate". For example,
and R1, 0xFFF ; R1 := R1 and 0xFFF
or R1, R2 ; R1 := R1 or R2
rshift R1, 13 ; R1 := R1 rshift 13
a) Suppose that a register R1 contains a 6 bit unsigned number in
bits 7 though 12. Write a sequence of assembly language instructions
that will store these 6 bits in the low order bits of another register R2
and set the high order bits of R2 to zero. R1 should remain unchanged.
b) Give a sequence of instructions that will take the 5 low order bits
in a register R2 and store them in bits 17 through 21 of R1, leaving
the rest of R1 unchanged. It is permissible to change R2.
3.a) Write a *recursive* function in some familiar higher-level language
(e.g., C) that computes the largest integer k such that, for any positive
integer n (input), 2^k <= n ; i.e., k is a largest integer approximation
to the logarithm (base 2) of n. The algorithm can be defined recursively
as follows:
log_2(n) = if n=1 then 0
else 1 + log_2(n/2)
Use at least one local variable in your function, even though this may not be
necessary.
b) Suppose that your function is implemented using a stack, stack pointer
register (sp), and frame pointer register (fp), as discussed in class.
Consider the call:
x = log_2(9);
Show the contents of the stack and pointer registers at *each* call of log_2,
starting with the one above, and after *each* return from the function.