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An arithmetic logic unit is a combinational logic component that performs selected arithmetic or bitwise operations on its input machine words. Its result and status outputs, such as a carry flag, depend on the operation control. A datapath may require a pass-through operation as well as addition, particularly when a barrel shifter feeds an operand.

A datapath comprises the processor registers, functional units and connections through which instruction operands and results move. Control signals select operand sources, operations, memory access and processor register writeback. Connecting a barrel shifter before an arithmetic logic unit permits shift-and-add operations in one pass, but puts their delays in series.

SP-relative addressing forms an effective memory address by adding an offset to the stack pointer. It accesses local variables, saved processor registers or other stack-frame data without dedicating a separate base processor register for each object. The supplied reference gives word-aligned SP-relative offsets from $0$ to $1020$, which corresponds to an eight-bit nonnegative field scaled by four.

In the modified datapath, select the stack pointer for the unshifted ALU input, the instruction immediate operand for the barrel shifter input, and ALU addition. The effective address can then be $\mathrm{SP}+(\mathrm{imm}\ll s)$. Scaling the immediate operand changes the reachable displacement range without storing a larger immediate operand. For example, an eight-bit field shifted by two reaches offsets through $255\times 4=1020$; shifting it by four reaches through $4080$, but only on a sixteen-byte grid. Larger range and finer address granularity are different properties, so the extra reach is not free arbitrary-byte addressing.

The parallel layout cannot feed a shifted immediate operand directly into its address-producing ALU in the same pass. The serial layout can. The actual immediate operand width and permitted shift encodings of a new instruction must be specified; the question does not fix them, so no particular enlarged instruction encoding is implied.

A useful additional mode is base plus scaled register indexing, with effective address $B+(I\ll s)$. For an array of four-byte elements choose $s=2$, use its base address on the unshifted ALU input and its index processor register on the barrel shifter input, then add. This forms an indexed machine word address in one datapath pass. An eight-byte element uses $s=3$.

With parallel ALU and barrel shifter outputs, shifting and adding require either separate instructions/cycles or another route from the barrel shifter to the ALU. The new serial connection supplies that route. This is an addressing mode capability, not a claim that the old instruction encoding already contains the new mode.