HW3 - Binary Multiplication

This is the first of two assignments in which you will write binary code for the simple machine you created a simulator for in lab. It is much simpler than the second one, and will take much less time. Both assume that you have understood that lab’s content well.

The instructions

icode Behaviors

0

rA = rB

1

rA += rB

2

rA &= rB

3

rA = read from memory at address rB

4

write rA to memory at address rB

5

do different things for different values of b:

b	action
0	rA = ~rA
1	rA = -rA
2	rA = !rA
3	rA = pc

6

do different things for different values of b:

b	action
0	rA = read from memory at pc + 1
1	rA += read from memory at pc + 1
2	rA &= read from memory at pc + 1
3	rA = read from memory at the address stored at pc + 1

In all 4 cases, increase pc by 2, not 1, at the end of this
instruction

7

Compare rA (as an 8-bit 2’s-complement number) to 0;

• if rA <= 0, set pc = rB
• otherwise, increment pc like normal.

Running programs

You should create two files

1. One you work with, that has comments and notes to keep you sane. Call this anything you like.

2. One you run and submit, which contains nothing by hex bytes separated by white space. You’ll submit this as a file named mult.binary

To test your code, do one of

python3 sim_base.py mult.binary

or

java SimBase mult.binary

or going to our online simulator and click the file upload button at the top of the page to load your mult.binary into the simulator’s memory.

Your task

Your code should

1. load the values in memory at addresses 0x01 and 0x03 into registers
2. compute the product of those values (i.e., multiply)
3. store the product at address 0xA0
4. halt once it is done

You should ignore overflow, so since 0x79 × 0x23 = 0x108B, the answer should be 8B. This is likely to happen automatically without your explicit planning for it. You may assume that neither multiplicand will be negative, but either or both may be zero.

Thus, if mult.binary begins __ 09 __ 0A then when it is finished it should have 5A in address 0xA0; if mult.binary begins __ 79 __ 23 then when it is finished it should have 8B in address 0xA0. We should be able to change the second and fourth bytes of your program to do other multiplications too.

Hints, tips, and suggestions

How to multiply

You may be familiar with fancier ways, but a simple definition of multiplication that will result in reasonable-to-write code is

Definition

x × y means the sum of y x’s; that is, x + x + x + … + x, where the number of xs is y.

You definitely want to make sure you can write working code for this in some language you know well before trying to convert that code into binary.

How to write binary

We suggest following these steps, carefully, saving the result of each in a file so you can go back and fix them if they were wrong:

1. Write pseudocode that does the desired task
2. Convert any for loops to while loops with explicit counters
3. Change any if or while guards to the form something <= 0
   • a <= b becomes a-b <= 0
   • a < b becomes a+1 <= b becomes a+1-b <= 0
   • a >= b becomes 0 >= b-a becomes b-a <= 0
   • a > b becomes 0 > b-a becomes b+1-a <= 0
   • a == b becomes a-b == 0 becomes !(a-b) == 1 becomes !!(a-b) <= 0
   • a != b becomes a-b != 0 becomes !(a-b) == 0 becomes !(a-b) <= 0
4. Add more variables to split multi-operation lines into a series of single-operation lines
5. Add more operations to convert ones not in the instruction set into ones in the instruction set
6. Change each loop into a pair of instructions, opening with “spot1 = pc” and closing with “if …, goto spot1”
7. Count the number of variables needed
   • If¹ it is ≤ 4, skip to step 10
   • else², continue with next step
8. Pick a memory address for each variable. Make these big enough your code is unlikely to get that big; for example, you might pick 0x80 though 0x80 + number of variables
9. Convert each statement that uses variables into
   1. register ← load variable’s memory
   2. original statement
   3. store variable’s memory ← register
10. translate each instruction into numeric (icode, a, b) triples, possibly followed by a M[pc+1] immediate value
11. turn (icode, a, b) into hex
12. Write all the hex into mult.binary

Debugging binary is hard. That’s part of why we don’t generally write code in binary. If you get stuck, you should probably try pulling just the part you are stuck on separate from the rest and test it until it works, then put it back in the main solution.

Submit

Submit via Gradescope.