1937

The Adder

Stibitz built the first one at home in 1937, out of scrap relays from the Bell Labs pile, strips cut from a tobacco tin, two dry cells and two torch bulbs. It added one bit, and one bit is genuinely complete: give it two inputs and it gives you a sum and a carry, needing nothing else. The trouble starts at two bits, because the second cannot begin until it knows what the first one carried.

One bit adds, and then the carry ties them all together

1 One bit, added, and the carry it produces

Three inputs, two outputs, no memory and nothing to wait for. Press any of them.

sum 0, carry out 0

Two ones give a sum of 0 and a carry of 1, which is the only interesting row: the answer does not fit, so part of it has to go somewhere else.

2 The carry, taken as an input to the next bit

That carry is an input to the bit on its left. It is the same signal, arriving one stage later, and it is the only thing connecting the bits to each other.

A, 0 to 255B, 0 to 255

3 Four of them chained, and the answer that is not ready yet

Eight of them, most significant first. A stage is marked when it received a carry, which is the same as saying it could not start until the stage to its right had finished.

4 The worst case, counted rather than asserted

The worst case is not an argument. Every pair of eight-bit numbers is 65,536 additions, which this browser can simply do.

This is why carry-lookahead exists: not to make addition cleverer, but to stop the answer to the left waiting on the answer to the right.

These ran in this browser when the page loaded. The second row is the expensive one: it adds every eight-bit pair there is and compares the result with ordinary arithmetic.

Each claim, whether it held, and the values behind it
claim	held	measured
each row is the parity of its inputs and a carry when two or more are set	yes	all 8 rows
all 65,536 eight-bit pairs match ordinary addition	yes	65,536 pairs, 0 wrong
one bit added alone needs nothing to its right	yes	1+1 gives sum 0 carry 1
a carry can travel the whole width, so the last bit waits for the first	yes	255+1 travels 8 stages, 1+0 travels 0
the worst case was found by trying every pair, not argued	yes	1 + 127 travels 8 of 8

What is real here, and what is not

The delays are stages, not seconds

This page counts how many stages a carry passes through, which is a real property of the circuit. It does not model time: no gate delay in picoseconds, no wire capacitance, no clock. A real ripple adder's speed depends on all three, and the number here is the thing they multiply, not the answer.

The full adder is a table, not a gate diagram

Addition here is eight rows looked up, not XOR and AND gates wired together. The rows are the same rows those gates produce, and the page checks that each one is the parity of its inputs with a carry when two or more are set. What you cannot see here is the gate count, which is where a real design spends its area.

The year is sourced; the month is not, and this page says so

The IEEE Computer Society's account of Stibitz places the kitchen-table adder in 1937 and describes the relays, the tobacco tin and the bulbs, but gives no month. Secondary accounts almost all say November, and the chronology sorts it there so that it sits before the 1945 entries rather than after them. That month is repetition, not evidence, and it is not printed anywhere on this page as though it were.

One bit is the Model K, and eight bits is not

Stibitz's machine added one bit and lit a bulb. The eight-bit chain on this page is the idea extended, not a model of anything he built, and the ripple arrangement it uses is the simplest of several. Carry-lookahead, carry-select and carry-save all exist to avoid exactly the walk this page makes you watch.

No sound

A relay clack per stage would be evocative and would measure nothing, because nothing here has a duration. The rule on this site is that a sound has to carry the measurement.

Sources

Logical Art builds interactive explanations of difficult machines.

The machines:

1935-1991 RangekeeperThe answer is on both sides of the equation, so it had to be a machine.
1964-1990s AbendThe loop you did not write, and the day it cost to get it wrong.
1971-1995 Line ModeYou could telnet to port 80 and be the browser, and then you could not.
1975 Front PanelA working 1975 Altair 8800 you program by flipping switches.
1980s 300 BaudA real dial-up modem and the BBS on the other end of it.
1994 WinsockThe two seconds after the modem stopped screeching, before anything worked.
2020s LLM LabTrain a tiny language model and watch every number as it learns.

Smaller pieces, on the studio itself: Morse, Baudot, Flip-Flop, Punch Cards, Interlace, Bitwise, The Adder, Stored Program, Two's Complement, Trigger, Bit, Nibble, Byte, Transistor, Score Reel, Hamming, Huffman, Core Memory, Hash Table, The Interrupt, CORDIC, CRC, Page Fault, ASCII, CPU Cache, Race, Fifteen Planes, B-tree, Backoff, Checkout, Diffie-Hellman, Zero Address, Fringes, LZ77, Signature, Z-Characters, Merkle Proof, Branch Prediction, Write-Ahead Log, Interleave, Eight Sprites, DNS, Floating Point, Slow Start, Longest Chain, JPEG, UTF-8, Masking, PageRank, Merge Collapse, Merkle DAG, Count Distinct.

A Logical Art machine by RoamingPigs, Inc. Built by Cisco Caceres in Las Vegas, NV.