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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.

Instruction pipelining divides execution into stages with stored intermediate state, allowing different instructions to occupy different stages simultaneously. The processor clock period is constrained by stage timing; moving a barrel shifter and arithmetic logic unit into the same stage can lengthen that stage's combinational critical path.

The following original schematic shows the two data organisations. Register-address, write-enable and memory controls are common background; the diagram highlights the changed combinational logic paths.

In the parallel design the result-source multiplexer selects either the arithmetic logic unit or barrel shifter. Its control is additional to the ALU function and shift amount. (i) Addition: read the two operands, select ALU addition and select the ALU result; the shift amount is irrelevant. (ii) Constant left bit shift: read the operand to be shifted, set the shift amount from the immediate operand and select the barrel shifter result; the ALU operation is irrelevant.

In the serial design the result comes through the ALU, so that result-source selection disappears. Its shift-amount control is now relevant to arithmetic as well. (i) Addition: set the barrel shifter to zero shift and select ALU addition, so its inputs are the unshifted processor register values. (ii) Constant left bit shift: set the requested shift and select an ALU operation that passes the shifted operand through. If the ALU lacks that operation, implement it or provide a selectable zero on its other input and add zero. This requirement should be stated, rather than assuming that an ordinary two-input add automatically performs a shift alone.

The ALU result can still supply the memory address. For a register-result instruction, enable processor register writeback and leave memory writes disabled. If the ISA requires shift carry flags, the flag-generation control must retain the barrel shifter's outgoing-bit information; blindly using a pass-through ALU's arithmetic carry is insufficient.

Scaled index addressing forms a memory address $B+sI$ from a base $B$ and index $I$. For element size $s=2^k$, a barrel shifter forms the displacement by a left bit shift before the arithmetic logic unit adds the base. This directly implements array indexing without a separate multiplication instruction.