Two Layers, One Extra Weight

Two layers are quantized with the same rule. A grid stored in $b$ bits has $2^b$ levels, evenly spaced, with the lowest level placed at the layer's smallest weight and the highest level at its largest weight. Every weight is then rounded to its nearest level.

• Layer A. Its weights all lie between $-0.3$ and $0.3$, and both ends are reached: the smallest weight is exactly $-0.3$ and the largest exactly $0.3$.
• Layer B. Exactly the same weights as layer A, plus one extra weight equal to $2.7$.

For either layer, call the worst-case rounding error the largest error that any weight between $-0.3$ and $0.3$ could receive.

Layer A is quantized to 4 bits. What is the smallest number of bits for layer B that makes its worst-case rounding error no larger than layer A's?