General Computer Science 320201 GenCS I & II Lecture ... - Kwarc

program of a computer (those that run, when the power is turned on and bootstrap the operating
system) is still given in special memory (called the firmware) that keeps its state even when power
is shut off. This is conceptually very similar to a bank of switches.
Example Programs
Example 448 Exchange the values of cells 0 and 1 in the data store
P instruction comment
0 LOAD 0 ACC : = P (0) = x
1 STORE 2 P (2): = ACC = x
2 LOAD 1 ACC : = P (1) = y
3 STORE 0 P (0): = ACC = y
4 LOAD 2 ACC : = P (2) = x
5 STORE 1 P (1): = ACC = x
Example 449 Let P (1) = a, P (2) = b, and P (3) = c, store a + b + c in data cell 4
P instruction comment
0 LOAD 1 ACC : = P (1) = a
1 ADD 2 ACC : = ACC +P (2) = a + b
2 ADD 3 ACC : = ACC +P (3) = a + b + c
3 STORE 4 P (4): = ACC = a + b + c
use LOADI i, ADDI i, SUBI i to set/increment/decrement ACC (impossible otherwise)
c○: Michael Kohlhase 277
So far, the problems we have been able to solve are quite simple. They had in common that we had
to know the addresses of the memory cells we wanted to operate on at programming time, which
is not very realistic. To alleviate this restriction, we will now introduce a new set of instructions,
which allow to calculate with addresses.
Index Registers
Problem: Given P (0) = x and P (1) = y, how to we store y into cell x of the data store?
(impossible, as we have only absolute addressing)
Definition 450 (Idea) introduce more registers and register instructions
(IN1, IN2 suffice)
instruction effect P C comment
LOADIN j i ACC : = P (INj +i) P C : = P C +1 relative load
STOREIN j i P (INj +i): = ACC P C : = P C +1 relative store
MOVE S T T : = S P C : = P C +1 move register S (source)
to register T (target)
Problem Solution:
P instruction comment
0 LOAD 0 ACC : = P (0) = x
1 MOVE ACC IN1 IN1: = ACC = x
2 LOAD 1 ACC : = P (1) = y
3 STOREIN 1 0 P (x) = P (IN1 +0): = ACC = y
c○: Michael Kohlhase 278
Note that the LOADIN are not binary instructions, but that this is just a short notation for unary
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