Sign extension?

[Archit N.C.]

In question 3.9 on the homework, it says that A_upper needs to be
adjusted because A_lower will be sign extended. But A_lower is a 16-bit
field (the 16 lower-order bits of A), and the immediate value in the lw
instruction is also 16 bits (as per the format of I-type instructions),
so why is any sign extension necessary in the first place?

Archit.

[Alan Lee]

The calculation in the load word instruction is performed using 32-bit
arithmetic because the base register is 32 bits even though the offset
is only 16 bits.

In question 3.9 on the homework, it says that A_upper needs to be adjusted
because A_lower will be sign extended. But A_lower is a 16-bit field (the 16
lower-order bits of A), and the immediate value in the lw instruction is also
16 bits (as per the format of I-type instructions), so why is any sign
extension necessary in the first place?
Archit.