Operator sizing - multiplication

What this digital design operator-sizing question tests

This is an easy digital design question that checks whether you understand the arithmetic properties of binary multiplication and how hardware implementations must allocate bit-width to avoid overflow. It's a foundational concept in hardware design and signal processing pipelines.

To solve operator-sizing problems like this, you need to reason about the maximum possible product of two numbers given their bit-widths, then determine the minimum output width needed to represent that result without loss of information. This is essential when specifying arithmetic units, designing data paths, and preventing silent data corruption in fixed-point systems.

• Bit-width of products in binary multiplication
• Overflow and saturation in hardware arithmetic
• Signed vs. unsigned multiplication