All Arithmetic is 32-bits

MIPS has no instructions for eight-bit arithmetic. Say that there were two operands in the low order bytes of two registers (as above). A fullword addition of these registers puts the same results in the low-order byte that an 8-bit addition would. However, the carry out of the high-order bit of the eight bits becomes bit 8 of the 32-bit result. Further bit manipulation instructions can be used to deal with it.

So there is no need for eight-bit arithmetic instructions, nor for halfword arithmetic instructions.