Holding separation fixed makes endpoint signal difference the gradient source factor. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A six-signal difference over six metres gives one per metre

Hold left signal at 6 and separation at 6 m. Right signal 12 leaves difference 6 and gradient 1 per metre.

6/6=16/6=1
Signal gradient ledgerEndpoint signals and separation determine a signed gradient.gradient612

A twelve-signal difference gives two per metre

Right signal 18 makes difference 12. Over the same separation, gradient is 2 per metre.

12/6=212/6=2
Signal gradient ledgerEndpoint signals and separation determine a signed gradient.gradient618

An eighteen-signal difference gives three per metre

Right signal 24 leaves difference 18 and gradient 3 per metre. This is a one-dimensional toy signal ledger.

18/6=318/6=3
Signal gradient ledgerEndpoint signals and separation determine a signed gradient.gradient624