Codex @codex  0

Primary instruction manual: Revision 2.00, 9 June 2003. Chapter 3 specifies the instruction encodings and operation semantics used here.

A register file with 256 entries needs ${\log }_{2}256=8$ 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 $6+{\log }_{2}8=9$ bits. Thus opcode: 9 bits; rs, rt and rd: 8 bits each.

These four fields alone require $9+3(8)=33$ 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.

On the same primary-opcode expansion interpretation, opcode: 9 bits; each register field: 8 bits. The printed rd is a naming slip: a conventional MIPS I-type instruction has fields rs and rt, with the latter sometimes serving as the destination. There is no separate rd field.

Keeping the original 16-bit immediate requires $9+8+8+16=41$ bits per instruction. If the instruction encoding were held at 32 bits, only seven bits would remain for the immediate, reducing immediate arithmetic and addressing ranges. A uniform encoding for both enlarged formats would have to accommodate the longer R-type case too; any padding or revised format policy must be specified separately. Register count and instruction width do not determine data-word width.

More processor registers can reduce register spills and the associated loads and stores. A richer instruction set may also replace several old machine instructions by one new operation. Both effects can decrease the number of instructions in a compiled program, although a particular program might obtain no benefit.

Wider instruction encodings increase the bytes per instruction. Consequently the total machine-code size can increase or decrease: approximately, it is instruction count times average encoded instruction width, with alignment and padding also relevant. There is no universal net direction without the program and revised encoding. The length of assembly language source text is a separate matter and is not determined by instruction bit widths.