Every earlier control gate lesson fixed the target at ten and scanned the controls or the tolerance instead; this scan holds the controls and tolerance fixed and moves the target. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Every earlier control gate held target fixed at ten

Chapters one, four, and six all kept target 10 fixed and only ever changed the controls or the tolerance. Here the same three controls 9, 10, and 11 and tolerance 1 stay fixed, but the target itself shifts to 9. The highest control now falls outside, so the row pass bit is 0.

119=2>1|11\,-\,9|=2>1
Control gateControls pass only inside the inclusive target window.targettolerancepasspassfail

The target itself decides which controls fit the gate

The controls and tolerance never change across these rows. Moving the target alone flips which controls sit inside the inclusive window, not just how many.

targetpass bitsA9(1,1,0)010(1,1,1)111(0,1,1)0\begin{array}{c|c|c}\text{target}&\text{pass bits}&A\\9&(1,1,0)&0\\10&(1,1,1)&1\\11&(0,1,1)&0\\\end{array}
Control gateControls pass only inside the inclusive target window.targettolerancepasspasspass

A target shifted the other way excludes the low control instead

At target 11, control 9 is now the one outside tolerance 1, while the other two controls still pass. The row pass bit is 0.

911=2>1|9\,-\,11|=2>1
Control gateControls pass only inside the inclusive target window.targettolerancefailpasspass