An MRI gradient is a checked position-to-frequency address rule. 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 gradient makes field a position address

Start with base field 1 tesla and gradient 1 tesla per metre.

B(x)=Bbase+GxB(x)=B_{\mathrm{base}}+Gx
MRI encodingA magnetic gradient makes position-specific frequency addresses.fieldfreqfieldfreqphasefieldfreqphasezero phase

Frequency follows the checked field

With gamma 4 hertz per tesla, the three fields 1, 2, 3 tesla give 4, 8, 12 hertz.

43=124\cdot3=12
MRI encodingA magnetic gradient makes position-specific frequency addresses.fieldfreqfieldfreqphasefieldfreqphasezero phase