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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 barrel shifter moves a machine word by a variable number of bit positions through a bounded-depth combinational logic circuit. For a $2^k$-bit machine word, cascade $k$ banks of multiplexers selecting optional shifts of $1,2,\dots ,2^{k-1}$. The binary shift-amount bits select the stages; the chosen distances add. Logical shifts fill vacated positions with zero, whereas bit rotations reconnect the discarded positions. A 32-bit logical barrel shifter can use five banks of 32 two-input multiplexers.

The combinational critical path is a longest propagation-delay path through a combinational logic circuit. Register-to-register clock timing also includes launch delay, setup time and clock uncertainty. Putting two functional units in series adds their dependent delays; operating them in parallel instead contributes the slower branch plus any subsequent selection delay.

A combinational logic device comparing two fixed-width binary representations. For unsigned inputs $a,b$, a two-output encoding is $L=1$ exactly when $a<b$ and $G=1$ exactly when $a>b$. Equality gives $(L,G)=(0,0)$; $(1,1)$ is unreachable. A one-bit implementation is $L=\neg a\wedge b$, $G=a\wedge \neg b$.

Digital electronics represents information by discrete signal levels. Combinational logic computes from current inputs; sequential logic also uses stored state.

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.

The likely effect in a single-cycle or unchanged pipeline-stage implementation is a longer combinational critical path and hence a lower maximum processor clock frequency. Previously the barrel shifter and ALU could work in parallel before result selection; the modified path can require both shift and addition before address or result use.

Ignoring common processor register and wiring delays, the relevant combinational logic contribution changes roughly from $\max (t_{\mathrm{ALU}},t_{\mathrm{shift}})+t_{\mathrm{mux}}$ to $t_{\mathrm{shift}}+t_{\mathrm{ALU}}$, with any additional input selection included as needed. The processor clock period must also cover processor register timing and the rest of the instruction path, potentially including memory access. Removing a multiplexer offsets some delay, so a numerical frequency change cannot be inferred without component timings. Pipelining, a faster implementation or another pre-existing bottleneck can alter the outcome; the changed serial dependence is the reason for the likely reduction.