What follows the maximum value?

Learning goals

• Calculate an addition that exceeds the stored width
• Distinguish wrapping from saturation

Store only the bits that fit

Adding one to 11 mathematically gives 100. count stores only the low two bits, 00, so its next state is zero. This counter cycles through values zero to three.

A counter that stops at three needs an explicit condition. Declaring two bits does not automatically make it stop at its maximum.

A new width needs new expectations

An unsigned N-bit counter represents zero through 2 to the power N minus one. A three-bit version wraps after seven. Check initialization, literal widths and expected waveforms along with the declaration.

First explain the original sequence 00 → 01 → 10 → 11 → 00. Then work on a copy, change the width and predict how the sequence will differ.