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Equation 1 · Part 10 · Chiplets and Advanced Packaging in Practice: Floorplanning, UCIe, and Thermal Co-Design

multiplication

Cost(P)  =  α⋅WL(P)  +  β⋅Tmax⁡(P)  +  γ⋅σmax⁡(P),\text{Cost}(\mathcal{P}) \;=\; \alpha \cdot WL(\mathcal{P}) \;+\; \beta \cdot T_{\max}(\mathcal{P}) \;+\; \gamma \cdot \sigma_{\max}(\mathcal{P}),
multiplication

What this part means

Multiply the quantities on either side.

Its job in the formula

Multiply the quantities on either side.

The passage around this formula

A floorplanning objective built to hold all three properties at once is naturally written as a weighted combination rather than a single term: Cost(P)  =  α⋅WL(P)  +  β⋅Tmax⁡(P)  +  γ⋅σmax⁡(P)\text{Cost}(\mathcal{P}) \;=\; \alpha \cdot WL(\mathcal{P}) \;+\; \beta \cdot T_{\max}(\mathcal{P}) \;+\; \gamma \cdot \sigma_{\max}(\mathcal{P}). where P\mathcal{P} is a candidate placement of dies on the carrier, WL is total interconnect wirelength, Tmax⁡T_{\max} is peak steady-state junction temperature anywhere in the assembly, and σmax⁡\sigma_{\max} is peak mechanical stress at any bonded interface. This is a schematic statement of the shape these tools optimize, not a reproduction of any one paper’s exact formula, but it makes the practitioner point concrete: whichever of α\alpha , β\beta , and γ\gamma a design team weights most heavily determines where dies actually land, and a…

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Learn the underlying idea

Multiplication scales one quantity by another. A dot, a cross, or adjacent symbols can indicate a product.

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Sources cited in the article section

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