Finite Conversion Relation Cross Scans

Reconstruction Error Three-Row Scan

Lower-edge reconstruction makes the error visible as input minus returned level. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

One-volt steps leave half a volt

Input 11/2 V with code 5 and LSB 1 V reconstructs 5 V, leaving error 1/2 V.

5⋅1 V=5 V,112 − 5=12 V5\cdot1\ \text{V}=5\ \text{V},\quad{11\over 2}\ -\ 5={1\over 2}\ \text{V}
Reconstruction error scanReconstruction and signed error labels are checked.recon=5 Verror=1/2 V

Half-volt steps land exactly

Input 11/2 V with code 11 and LSB 1/2 V reconstructs 11/2 V, leaving error 0 V.

11⋅12 V=112 V,112 − 112=0 V11\cdot{1\over 2}\ \text{V}={11\over 2}\ \text{V},\quad{11\over 2}\ -\ {11\over 2}=0\ \text{V}
Reconstruction error scanReconstruction and signed error labels are checked.recon=11/2 Verror=0 V

Another between-edge input leaves the same half volt

Input 7/2 V with code 3 and LSB 1 V reconstructs 3 V, leaving error 1/2 V.

3⋅1 V=3 V,72 − 3=12 V3\cdot1\ \text{V}=3\ \text{V},\quad{7\over 2}\ -\ 3={1\over 2}\ \text{V}
Reconstruction error scanReconstruction and signed error labels are checked.recon=3 Verror=1/2 V