Past exam of the year 1 of the computer science course of the University of Oxford / 2014 / Digital systems, linear algebra, introduction to formal proof / 1 / b / Solution

Add zero extension alongside sign extension, and a multiplexer controlled by a new signal ExtSign to select between them before the existing immediate-input connection. Equivalently, make the extender itself selectable:Decode ori to ExtSign=0, RegDst=0, ALUSrc=1, RegWrite=1 and ALUFunc=OR. The arithmetic logic unit then performs bitwise OR between $y$ and the zero-extended immediate operand and writes the result to $x$. Extend the arithmetic logic unit's control decoding if OR was not already available. Decode addi to ExtSign=1; the new signal is irrelevant for MIPS R-type instructions because ALUSrc=0.

Zero extension matters even when the most significant immediate bit is one: ori with 0x8000 must only affect the low half of the destination, whereas sign extension would incorrectly force every high bit to one.^[ref]