Accepted and rejected Bragg rows are exact path ledgers. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
First-order equality accepts
Order 1 with wavelength 6 m and plane spacing 3 m gives path left 6 m, path right 6 m, and accepted bit 1.
nλ=1⋅6=6m=2d=2⋅3=6m,accepted=1
Second-order equality also accepts
Order 2 with wavelength 4 m and plane spacing 4 m gives path left 8 m, path right 8 m, and accepted bit 1.
nλ=2⋅4=8m=2d=2⋅4=8m,accepted=1
A nearby wavelength still rejects
Order 1 with wavelength 4 m and plane spacing 3 m gives path left 4 m, path right 6 m, and accepted bit 0.