Discussion
What is the range of instruction addresses to which conditional branches, such as beq and bne can branch in MIPS ?
Answer: A
The range is +/- \(2^{17}\) bytes.
MIPS beq and bne are I-type instructions with a 16-bit signed immediate. The offset counts words (instructions), not bytes, and is added to PC + 4 after being shifted left by 2. A 16-bit signed field spans about \(\pm 2^{15}\) words, and since each word is 4 bytes:
\[ \pm 2^{15} \times 2^{2} = \pm 2^{17} \text{ bytes} \]
\(\pm 2^{16}\) would ignore either the sign bit or the word scaling, \(2^{32}\) is the whole address space, and \(2^{8}\) is far too small for a 16-bit field.
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