Repetition and Counters · Lesson 15 of 30 · about 12 minutes

Sum One to N

Keep an accumulator separate from the loop counter.

01 / Explain

Understand the idea

An algorithm is a repeatable method for solving a problem. To sum 1 through N, begin with total zero and add the current counter during each iteration. The total and counter serve different roles and need separate registers.

An invariant is a statement that remains true as the algorithm runs. After k iterations, the total is 1 + … + k. At zero iterations it is zero. Inspect this relation in the trace instead of guessing from the final answer.

02 / Try

Watch it happen

The running totals are 1, 3, 6, and 10. Only the final total is printed.

LOAD 1 R1
LOAD 0 R2
LOOP 4
LOAD R2
ADD R1
COPY R0 R2
LOAD R1
ADD 1
COPY R0 R1
RETURN
LOAD R2
PRINT
HALT

Use Step to follow one instruction at a time. You can change the example and replay it.

03 / Challenge

Make it work

Read N from 0 through 10. Use a loop to print the sum 1 + 2 + … + N. Print 0 for N = 0.

The checker runs your current editor program in a fresh machine for each of 3 test cases. It supplies inputs and seeded memory itself; the lab’s current output and memory do not decide your result.

INPUT
COPY R0 R3
LOAD 1 R1
LOAD 0 R2
LOOP R3
  # Add counter to total, then increment counter.
RETURN
LOAD R2
PRINT
HALT

Need a hint?

Reload R2 before adding R1, then save the new total back to R2.

Reveal a worked solution

Read the program, predict each instruction’s effect, then step through it in the lab.

INPUT
COPY R0 R3
LOAD 1 R1
LOAD 0 R2
LOOP R3
LOAD R2
ADD R1
COPY R0 R2
LOAD R1
ADD 1
COPY R0 R1
RETURN
LOAD R2
PRINT
HALT

Emoji program

Type LOAD, ADD, or another opcode then Space to insert emoji. Ctrl/⌘ + Enter runs or pauses; Escape pauses; Ctrl/⌘ + ] indents. Tab moves focus. Labels use a colon. Jumps use zero-based instruction addresses.

INPUT
COPY R0 R3
LOAD 1 R1
LOAD 0 R2
LOOP R3
  # Add counter to total, then increment counter.
RETURN
LOAD R2
PRINT
HALT

Instruction map and breakpoints (0)

Breakpoints stop before an instruction. Run resumes past the stopped breakpoint once; Step executes it directly. Editing source clears old breakpoints and machine state.

Use Number

CPU registers

R0: 0
R1: 0
R2: 0
R3: 0
R4: 0
R5: 0
R6: 0
R7: 0

Program counter (PC): 0
Stack pointer (SP): 255
Flags: Zero: off · Negative: off · Overflow: off
Delay request: 0 ms

Stacks and loop frames

SP = 255 − data depth − call depth. The stack is separate from memory.

Data stack (bottom → top)

Empty

Call return addresses (bottom → top)

Empty

Loop frames

Empty

Output and input

Run a PRINT instruction to see output.

Queued input: Empty

Memory · 256 bytes · 0 nonzero

Each cell shows address:value. R = read this step; W = written this step. Select a cell to inspect or initialize it before execution. Use arrow keys to move, Home/End for the row, and Ctrl/⌘ + Home/End for the whole memory.

Execution trace · 0 entries

Recent entries below. Inspect any zero-based index to see complete detached before/after state.

Check your challenge

You can run this check any time. Every case must pass to record completion.

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