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Arithmetic and instruction pipeline

Short answer

An arithmetic pipeline divides a floating-point add into segments for parallel operation; e.g., X+Y normalised in 4 segments. An instruction pipeline overlaps fetch, decode, operand fetch, and execute of successive instructions; 4 instructions take 7 cycles instead of 16. Both increase throughput by filling pipeline stages simultaneously.

Explain the arithmetic pipeline and instruction pipeline with example.

Arithmetic pipeline

It splits an arithmetic operation into segments, each done in separate hardware, so a new operation can enter every clock. Example, floating-point addition in four segments: (1) compare exponents, (2) align mantissas, (3) add/subtract mantissas, (4) normalise.

 X=0.9504x10^3 , Y=0.8200x10^2
 1) exponent difference = 1
 2) Y -> 0.0820 x 10^3
 3) sum = 1.0324 x 10^3
 4) normalise -> 0.10324 x 10^4

While pair 1 is being added, pair 2 is being aligned and pair 3 is being compared, giving one result per clock after the first. It is used for vector and scientific processors.

Instruction pipeline

It overlaps the steps of different instructions. A four-segment example: FI (fetch instruction), DA (decode and address calculation), FO (fetch operand), EX (execute).

Segment |  1  2  3  4  5  6  7
------------------------------
FI      | I1 I2 I3 I4  .  .  .
DA      |  . I1 I2 I3 I4  .  .
FO      |  .  . I1 I2 I3 I4  .
EX      |  .  .  . I1 I2 I3 I4

For 4 instructions, k + n - 1 = 4 + 4 - 1 = 7 clocks instead of 16. Delays arise from data dependency, branches and resource conflicts, solved by forwarding, stalls, branch prediction and delayed branch.

Difference

Arithmetic pipelineInstruction pipeline
Overlaps steps of one arithmetic operationOverlaps steps of instruction execution
Stages are arithmetic sub-operationsStages are fetch, decode, operand fetch, execute
Used in floating point units, vector machinesUsed in all modern CPUs
Few hazardsBranch, data and structural hazards

✓ Answer checked by Claude Opus 5.5 (high effort)

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