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 finish until it knows what the first one carried.
New to logic gates? Start here
Everything is a switch
A Boolean signal has two logical values, usually called 0 and 1. AND is true when both inputs are true, OR when either is true, and NOT reverses the value. Switches make a useful first picture of these operations.
Combinations of those operations can add, compare and select. A circuit that remembers also needs a way to keep state. This is a vocabulary for digital logic; it does not describe analogue signals or quantum amplitudes.
The machine for this idea on its own is Flip-Flop, if you would rather press it than read about it.
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. That is the row that matters: 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.
3 Eight 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. The readout counts the longest generator-and-propagator chain; the markings also show a final stage that consumes a carry without passing it on.
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.
| 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 + 255 travels 8 of 8 |
What is real here, and what is not
The carry chain is a span, not a delay
The readout counts the longest connected carry-producing chain: one stage generates a carry, and following stages with unlike input bits propagate it. Another generator starts a separate chain; a stage with two zero inputs ends it. Thus 128 plus 128 spans one stage, 255 plus 1 spans eight, and 255 plus 255 has eight independent one-stage generators. The old readout counted the position of the highest active carry instead, calling 128 plus 128 an eight-stage chain. This count excludes the final sum-consuming stage and is not a gate-latency measurement. No gate delay, capacitance or clock is modelled.
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
- IEEE Computer Society, Computer Pioneers: George Robert Stibitz. The 1937 kitchen-table adder, the scrap relays and what it was built from. Fetched and checked: it dates the work to 1937 and names no month.
- G. R. Stibitz, Complex computer, US patent 2,668,661. Bell Labs relay arithmetic described by the man who built it.
- Logical Art, the studio this belongs to.