MIPS I instruction immediate field

Question

The field is used by arithmetic and conditional branch instructions.

First question is:

What would be the range of values which can be stored in an immediate arithmetic instruction and conditional branch?

Second is:

if a MIPS processor has 64 registers, how would you change the immediate instruction format to reference these registers? How would I draw and label the format?

Answer 1

Part 1:

As illustrated by this diagram:

The I-Type instruction has 16 bits reserved for the immediate field. This of course means that the immediate field can take on 2¹⁶ possible values. If we consider that the immediate field can be positive or negative (1 bit is used for the sign) we can see that the max would be 2¹⁵ - 1 and the min would be −(2¹⁵ - 1).

andi, ori, and xori zero-extend the immediate (0 to 2¹⁶ - 1), while all other MIPS I-type instructions sign-extend the immediate/offset.

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Part 2:

Again, looking at the diagram above we can see that the rs and rt registers are specified with 5 bits. This is because there are 32 registers in the mips instruction set — i.e. 2⁵. If there were instead 64 registers, both the rs and rt fields would need to be 6 bits long, thus leaving only 14 bits for the immediate field.