Past exam of the year 1 of the computer science course of the University of Oxford / 2021 / Digital systems, linear algebra, introduction to formal proof / 2 / c / Solution 2026-10-25
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A register file with 256 entries needs bits per register index. Under the intended assumption that eight times as many instructions are obtained by expanding the primary opcode field, its width grows from six to bits. Thus opcode: 9 bits; rs, rt and rd: 8 bits each.
These four fields alone require bits, already exceeding a 32-bit instruction encoding. Retaining the five-bit shift amount and six-bit function field of a MIPS R-type instruction gives 44 bits. The processor's data word need not become wider merely because it has more registers.
The opcode conclusion is conditional: MIPS also uses secondary function fields, so an eightfold increase in the number of semantic operations does not by itself force a nine-bit primary opcode. That is the straightforward field-expansion interpretation of this exercise.
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