Converter Boundary Depth Scans

Reconstruction Error Sign Three-Row Scan

The signed error convention matters around the 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

Input below the returned level gives negative error

Input 9/2 V minus reconstruction 5 V gives error -1/2 V.

92 V − 5 V=−12 V{9\over 2}\ \text{V}\ -\ 5\ \text{V}={-1\over 2}\ \text{V}
Signed reconstruction error scanError is input minus reconstructed level.recon=5 Verror=-1/2 V

Input at the returned level gives zero error

Input 5 V minus reconstruction 5 V gives error 0 V.

5 V − 5 V=0 V5\ \text{V}\ -\ 5\ \text{V}=0\ \text{V}
Signed reconstruction error scanError is input minus reconstructed level.recon=5 Verror=0 V

Input above the returned level gives positive error

Input 11/2 V minus reconstruction 5 V gives error 1/2 V.

112 V − 5 V=12 V{11\over 2}\ \text{V}\ -\ 5\ \text{V}={1\over 2}\ \text{V}
Signed reconstruction error scanError is input minus reconstructed level.recon=5 Verror=1/2 V