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Equation 1 · Part 1 · Comparing the Main Approaches to AI Memory Systems and the Bandwidth Wall

Symbol B

B  ≈  W⋅feff,B \;\approx\; W \cdot f_{\mathrm{eff}},
BB

What this part means

B is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

B is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

Bandwidth in particular has a hidden physical driver that explains why these four approaches look so different from one another: pin count. A memory bus’s raw bandwidth is well approximated by B  ≈  W⋅feffB \;\approx\; W \cdot f_{\mathrm{eff}}. with W the bus width in bits and fefff_{\mathrm{eff}} the effective transfer rate per pin. For a conventional DIMM interface, W is set by the number of package pins a processor can spare and a printed-circuit board can route, and that number has a hard physical ceiling — DDR5 alone specifies 288 pins per channel, and adding channels for more bandwidth becomes markedly more expensive under a CPU package’s pin budget [ 6 ] . Once W is capped by the board, the only lever left is…

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