Equation 1 · Part 13 · AI Accelerator Architecture in 2035: Scenarios, Signals, and Falsifiable Predictions

Denominator: B(t)

\frac{F(t)}{B(t)} = \frac{F_0}{B_0}\left(\frac{r_F}{r_B}\right)^{t/2}

B(t)

What this part means

The complete quantity below the fraction bar; it must be nonzero for this division.

Its job in the formula

B(t) occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

Full expressionDenominator: B(t)Article meaning

The passage around this formula

The structural fact behind every accelerator roadmap for a decade has been that peak arithmetic throughput has scaled roughly three times every two years while DRAM bandwidth has scaled roughly 1.6 times and interconnect bandwidth roughly 1.4 times over the same interval [ 1 ] . Analysis. Extending those three exponents unchanged from a 2024 baseline to 2035 — eleven years, or 5.5 doubling periods at the two-year cadence the source measures — gives a compact way to see how much the imbalance would compound if nothing structural intervenes: $\frac{F(t)}{B(t)} = \frac{F_0}{B_0}\left(\frac{r_F}{r_B}\right)^{t/2}$ . With $r_F$ $\approx$ 3.0 and $r_B$ $\approx$ 1.6 for DRAM bandwidth, ( $r_F$ / $r_B$ )^{5.5} = (1.875)^{5.5} $\approx$ 32 : the ratio of peak…

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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

Open the illustrated fractions: division written vertically guide →

Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.