1.2.3(c), 1.2.4(c), 2.2.1(a)Software and DevelopmentCore

LMC Counted Loops and Debugging

An assembly loop must implement its own counter, condition and jump. Build a small trace to show that it terminates and performs the required number of updates.

35 min Assembly and Addressing

What you'll be able to do

Trace an LMC accumulator-based loop
Write and explain a counter update and back branch
Test zero and one as boundary inputs

State the loop contract

The program below accepts a non-negative integer n and outputs 1+2+...+n, provided the counter and sum fit the chosen LMC model. Input zero gives zero. sum starts at zero and counter stores n. The accumulator is repeatedly reloaded because each task reuses it for a different purpose.

At the top of each iteration, counter tells us how many positive terms remain. BRZ done checks the zero case before adding a term. The body adds counter to sum, stores the new sum, subtracts one from counter, stores it and branches back. Both stored values are needed because there is only one accumulator in this model.

Trace the state that persists

For n=3, successive counter values at loop entry are 3, 2, 1 and 0. After the three bodies, sum is 3, then 5, then 6. The zero entry branches straight to done, where loading sum restores the value to be output. The accumulator may hold a counter or intermediate result during the loop; that is not necessarily the final answer.

A loop invariant can describe why the calculation works: sum contains the terms already removed from the countdown, while counter identifies the next term. Progress follows because every positive counter is reduced by one, and the allowed inputs eventually reach zero. Negative input would not meet that termination argument and is outside this program’s contract.

Use boundary tests to expose faults

For input zero, no body should run and output should be zero. For input one, exactly one body should run and output should be one. If the zero check is moved after the body, the program may execute an unwanted update before discovering there is nothing to add. If STA counter is omitted, the stored counter never decreases.

When debugging, distinguish a wrong operation from a missing store or wrong branch target. Trace the program counter when a loop repeats unexpectedly. A mathematically correct sum can still overflow a limited mailbox, so the input contract includes a range bound. A simulator’s exact representation of out-of-range values should not be assumed to rescue an invalid input.

LMC assembly

        INP
        STA counter
loop    LDA counter
        BRZ done
        ADD sum
        STA sum
        LDA counter
        SUB one
        STA counter
        BRA loop
done    LDA sum
        OUT
        HLT
counter DAT 0
sum     DAT 0
one     DAT 1

Scroll horizontally to see the full code or table.

Original countdown summation; non-negative input and a representable total are preconditions.

Work through the problem

Attempt the task before opening its worked response. Record each change of state, explain the rule used, and check the result against the original requirements. Code examples labelled Python 3 use that language’s conventions; pseudocode states its own assumptions.

Example 1Trace input 4 using counter and sum at each completed body.

1Start counter=4,sum=0; first body leaves counter=3,sum=4.

2Further bodies leave (2,7), (1,9), then (0,10); the zero check exits.

AnswerOutput 10.

Example 2Explain the effect of removing STA counter after SUB one.

1Subtraction changes only the accumulator.

2The next LDA counter reloads the unchanged positive value, so the loop does not progress towards zero.

AnswerThe counter update must be stored; otherwise positive input causes repeated looping.

Common mistakes to avoid

Changing a value only in the accumulator when later code reloads its mailbox.

Store persistent state updates before looping.

Testing only a typical positive input.

Include zero, one and the largest permitted safe input.

Key takeaways

An assembly loop needs explicit state and control.
A stored counter must be updated for progress.
Boundary cases and range assumptions matter.

Test yourself

Answer a few questions, then review anything you missed.

Next step

Keep practising

Start with the quiz above to check the key ideas. You can also choose another topic from the practice library.

Browse practice topics

Related lessons

All 3 lessons

INP STA counter loop LDA counter BRZ done ADD sum STA sum LDA counter SUB one STA counter BRA loop done LDA sum OUT HLT counter DAT 0 sum DAT 0 one DAT 1