ICSI 404 – Assignment 2: ALU Design
The second programming assignment builds on the first to complete an ALU design. Now that we have
created a long-word simulator with bitwise logical operations and bit-shift capabilities, we can extend it
to simple logic-based arithmetic processing, namely addition and subtraction. We need to remember
that logic-based addition (subtraction is only addition of the 2’s complement of the integer subtracted)
works solely on the bit-vector patterns – without any concern whether the operands are unsigned or
signed. The only difference is made in the interpretation of the bit-vector and implementation of the
overflow logic for the unsigned or signed cases.
The other aspect of ALU design is that we need to decide upon a set of arithmetic and logic operations
the ALU will perform on the operands (long-words in our case). We also need a few encoded control
bits as a chooser for the ALU operation to be triggered. As noted in our discussions about assembly and
machine instructions, these control bits come from either the opcode field of the machine instruction or
the secondary function part, in case multiple operations are grouped to share an opcode. To keep it
simple, all instructions using the ALU will have distinct opcodes in our design.
For our 32-bit machine, the ALU class implementation must follow these specifications:
- The ALU class must be a new class that does not inherit from (i.e., extend) any other class.
- A ALU object must be instantiated before it can perform an operation. In other words, you should
not plan on developing ALU as a static class. There are two reasons behind this choice. First, most
modern general-purpose CPUs have multiple ALUs to exploit instruction level parallelism. Thus, you
may like to extend your code later to emulate a more featureful CPU with multiple ALU instances.
The second and more compelling reason is that the following boolean flags must be maintained for
an ALU instance. The values of these flags are to be automatically updated after every operation,
based on the specifications below:
The zero flag (ZF) should be set to 1 (true) when the ALU operation results in a long-word
valued 0 (i.e., all bits are cleared). It should not matter whether the operation in arithmetic
(add/subtract) or logical (including bit shifts).
The negative flag (NF) should be set to 1 (true) when the ALU operation results in a long-
word that is considered negative under 2’s complement signed interpretation (i.e., MSB is
negative). It should not matter whether the operation in arithmetic (add/subtract) or logical
(including bit shifts).
The carry-out flag (CF) should be set to 1 (true) when ALU operation results in a carry-out
from the MSB position. This flag is meant to indicate an overflow resulting from unsigned
addition, but this flag must be computed for every add/subtract operation as the machine
opcode only works on bit-vector without considering their interpretation.
The overflow flag (OF) should be set to 1 (true) when ALU operation results in an overflow
condition based on 2’s complement arithmetic. Recall that for ripple-carry addition, this is
indicated by a mismatch (XOR) in the carry-in and carry-out bits in the MSB position. While
we expect none of the logical operations to set this bit, there is only one exception. The left
shift operation, with shift amount 1-bit, is often substituted for a multiplication with 2. This
is particularly useful for shift-and-add multiplication. When such a multiply-by-2 operation
flips the sign of the result, it clearly is an overflow, and the overflow flag must be set. While
the same situation is also possible for multiple-bit left-shift (k-bit shift is multiplying with 2k),
the overflow flag is not to be set there as one cannot pinpoint after exactly how many bit
shifts causes the overflow.
The exact way how to store these four flags is left to you. In the simplest implementation, you may
like to keep four boolean variables. However, real CPU hardware dedicate a whole register (as long
as the machine word) to store all necessary flags, including the four just described. This register goes
by different names such as flag register, status register or program status word (PSW). Some bits of
the PSW may be left unused. So, another option is to keep a long-word for the PSW among the data
field of the ALU object and use only the least significant four bits (0-3). This second approach mimics
the hardware implementation more closely. Since it is easy to forget which bit is used for which flag,
use of enum and the ordinal method of its constant instances may come handy. - The ripple carry adder logic, as discussed in class, must be used for both addition and subtraction
of long-words. In other words, you may not use Java’s built-in add/subtraction by extracting the
value of the operands from the representative bit-vectors using getSigned or getUnsigned
methods, and then injecting the result back using set method. The bit-by-bit addition logic makes
use of Boolean XOR (since we are using boolean type for a bit). You may implement this any way
you like. While you can compose ‘&&’ and ‘||’ operators to create logical XOR, there are simpler
alternatives such as making use of the bitwise ‘^’ operator or simply comparing two Boolean values
using ‘!=’ . In any case, you need a Boolean argument (apart from the two long-words) serving as the
carry-in to the LSB (which is ‘0’ for addition and ‘1’ for subtraction, assuming the bits are flipped for
the operand being subtracted). The ripple-carry adder method should look somewhat like:
private LongWord rippleCarryAdd(LongWord a, LongWord b,
boolean cin)
Note that this method should be responsible for setting the CF and OF flag bits. Also, it should be
made private for internal use by the ALU when the control bits trigger an add/subtract operation.
The ALU’s public interface should only involve control codes and necessary operands as inputs and
the result as well as flag bits as outputs.
- You must create the public interface for your class by implementing the following methods:
a) At creation, the flag bits, or the status register (depending on your implementation choice) must
be cleared (initialized to ‘0’).
b) Implement the accessor(s) based on your implementation of the condition flags. You may either
have an accessor for each of the flags (e.g., getZF, getNF, getCF and getOF) or have a single
accessor for the whole program status word (getStatus). When your CPU needs to check the
Boolean value of a flag (in the next assignment), it needs to extract the correct bit in the second
case. The same applies to your tester program in the current one.
c) Implement the only mutator which performs the ALU operation based on the given control
code. The prototype may look like
public LongWord operate(int code, LongWord op1, LongWord op2)
Note that this mutator method not only returns the result of the ALU operation as a long-word,
but also has an appropriate side-effect on the condition flags. The control codes must be exactly
as the following table – the machine opcodes will not match otherwise:
Operation
Machine
opcode
ALU
code
OP1 OP2 ZF NF CF OF
AND 1000 000 (0) Operand1 Operand2 if zero if -ive X X
OR 1001 001 (1) Operand1 Operand2 if zero if -ive X X
XOR
NOT
1010
1010
010 (2)
010 (2)
Operand1
Operand
Operand2
11…1 (-1)
if zero
if zero
if -ive
if -ive
X
X
X
X
ADD 1011 011 (3) Operand1 Operand2 if zero if -ive Cout(31) Overflow
SUB 1100 100 (4) Operand1 Operand2 if zero if -ive Cout(31) Overflow
SLL 1101 101 (5) Operand amount if zero if -ive X amontt=1
and
sign-flip
SRL 1110 110 (6) Operand amount if zero X X X
SRA 1111 111 (7) Operand amount if zero if -ive X X
In all methods, you must validate inputs where appropriate.
You must provide a test file (TestALU.java) that implements void runTests method and call it from
your main, along with your existing tests. As with the other tests, these tests must be independent of
each other and there must be reasonable coverage. You cannot reasonably test all of the billions of
possible combinations, but you can test a few representative samples.
In case you have updated the source code in your LongWord.java file, please make sure to include the
compatible updated version.
You must submit buildable .java files for credit.