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Algorithms with State · Lesson 17 of 30 · about 15 minutes

The Fibonacci Sequence

Keep two previous values and update them in a safe order.

01 / Explain

Understand the idea

Starting with 1 and 1, each Fibonacci value is the sum of the previous two. R1 holds the next value to print and R2 holds the value after it. After printing R1, calculate their sum and move the pair forward.

Update order matters. Replacing R1 too early can lose a value still needed for the sum. A temporary register or the still-live R0 result keeps the transition safe. Use a bounded count, not an equality check against a number the sequence may never reach.

02 / Try

Watch it happen

Expect 1, 1, 2, 3, 5, 8, 13, 21. Eight iterations make the sequence stop at a known point.

LOAD 1 R1
LOAD 1 R2
LOOP 8
LOAD R1
PRINT
ADD R2
COPY R2 R1
COPY R0 R2
RETURN
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 8. Print the first N Fibonacci values, starting 1, 1. Print nothing for N = 0.

The checker runs your current editor program in a fresh machine for each of 4 test cases. It supplies inputs and seeded memory itself; the lab’s current output and memory do not decide your result.

INPUT
COPY R0 R4
LOAD 1 R1
LOAD 1 R2
LOOP R4
  # Print current; calculate and move the pair forward.
RETURN
HALT
Need a hint?

ADD R2 leaves the new sum in R0, so COPY R2 R1 can preserve the old second value first.

Reveal a worked solution

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

INPUT
COPY R0 R4
LOAD 1 R1
LOAD 1 R2
LOOP R4
LOAD R1
PRINT
ADD R2
COPY R2 R1
COPY R0 R2
RETURN
HALT

Emoji CPU lab

Ready · 0 cycles

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.

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.

    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.

    Reset before initializing memory. Stored values wrap to 0–255.
    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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