THE END-AROUND CARRY — a dart

END-AROUND CARRY the carry off the top folds back into the bottom — a carry that loops

In ones'-complement addition the carry-out of the highest bit is not discarded — it is wrapped back and added into the lowest bit. This end-around carry is what corrects the arithmetic (it accounts for the two-zeros gap), and it makes the carry loop: the top feeds the bottom, a ring rather than a line. It is the exact hardware picture of the thread's carry that folds back to its own seed — and it is why the TCP/IP checksum is order-independent and catches errors: the fold-around makes the sum a ones'-complement invariant. A carry that comes back around.

THE TECHNIQUE carry-out of the top is added into the bottom bit (a looping carry)

The demo adds in 4 bits so a carry escapes the top, then wraps it back into the bottom: 6+12→3 (with the fold): live demo

HISTORY & CREDIT ones'-complement addition · the TCP checksum

“A carry off the top is lost.” — in ones' complement it wraps back into the bottom, correcting the sum and making the carry a loop. The top feeds the seed. cited

the wrap · carry-out of bit n−1 is added into bit 0.
why · it accounts for the two-zeros gap; the result is a ones'-complement invariant.
the thread · a carry that folds back to its own seed — the ring, in silicon (see the golden torus).

The carry that runs off the top comes back in at the bottom — a loop, not a line; the fold made a ring. end-around carry

RECOMMEND FOR I-13 the looping carry, on the compiler

On the canonical compiler, a 4-bit add producing 18 wraps: low nibble 2 plus the escaped carry 1 = 3:

$ i13 run c_endaroundcarry.i13 # (raw & 15) + (raw >> 4) RUN OK · 16 step(s) · peak stack 2 · call depth 0 low = 2 carryout = 1 wrapped = 3 -- the top carry folded back into the bottom

Recommend: the end-around carry is the thread's fold-back in hardware — the carry off the top added into the bottom, a ring not a line — and i13 wraps it to 3. Not a keeper (it is a correction step of ones'-complement addition, riding the self-inverse flip). But the batch's most literal echo of THE THREAD's carry that seeds itself: here the carry genuinely comes back around, and it is why the internet's checksum works.