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88377c8
fix some typos, formatting and missing alt text
Alejandro-Casanova Jun 23, 2026
3930a2f
improve schematic visualization using png instead of svg
Alejandro-Casanova Jun 23, 2026
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18 changes: 9 additions & 9 deletions examples/chapter16_08/readme.md
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@@ -1,4 +1,5 @@
# Example Chapter16_08 (advanced level)

## Generate and Display 128-bit Random Prime Numbers

This advanced example uses a self-made pseudo-random electronic
Expand Down Expand Up @@ -34,7 +35,7 @@ from Newhaven Display International. The display
is 40 characters in width by 4 lines and is, in fact,
controlled as two individual displays packed together.

The realease version of this software is intended to run on our target
The release version of this software is intended to run on our target
with the 8-bit microcontroller, as shown below.
On this system, it takes approximately $15~\text{s}$ on average
to find each single new pseudo-random 128-bit prime.
Expand All @@ -51,10 +52,10 @@ project uses
[Boost.Multiprecision](https://www.boost.org/doc/libs/1_82_0/libs/multiprecision/doc/html/index.html)
for its 128-bit integer representation and independent primality testing.

This advanced example's software running on an 8-bit micrcocontroller
This advanced example's software running on an 8-bit microcontroller
exhibits a fascinating combination of elementary electronics,
real-time C++ object-oriented and template programming,
and the inate elegance and beauty of pure mathematics.
and the innate elegance and beauty of pure mathematics.

## Hardware Setup

Expand All @@ -71,7 +72,7 @@ of the breadboard. The $12~\text{V}$ supply (center left) stems from a classic L
voltage regulator, from which TTL $+5~\text{V}$ (upper left) is also derived for
the MCU and logic power rail.

![](./images/board16_08.jpg)
![View of hardware setup](./images/board16_08.jpg)

In this particular image,
the system has accumulated a few hundred pseudo-random prime
Expand All @@ -83,21 +84,20 @@ with the prime number theorem.
The electronic subcircuit used for creating the random digitized noise
is sketched below.

![](./images/circuit16_08.svg)
![Schematic view of the random noise generator subcircuit](./images/circuit16_08.png)

The oscilloscope image below shows a small snapshot
of the random digitized noise from this circuit.
The square-wave-like pulses result from digitizing the random signal
above/below $0~\text{V}$. This is done with an op-amp and rudimentary logic,
as shown in the circuit.

![](./images/signal16_08.jpg)
![View of the generated noise on oscilloscope](./images/signal16_08.jpg)

## Deep Connection to the Prime Number Theorem

Recall the prime counting function
previously encountered in Example Chapter03_02
[here](https://github.com/ckormanyos/real-time-cpp/tree/master/examples/chapter03_02#prime-counting-function).
previously encountered in Example [Chapter03_02](https://github.com/ckormanyos/real-time-cpp/tree/master/examples/chapter03_02#prime-counting-function).
The prime number theorem known from mathematical number theory
postulates that the prime counting function $\pi(x)$ for large $x$
asymptotically and approximately approaches
Expand Down Expand Up @@ -148,7 +148,7 @@ $$
\left(\frac{2}{3}\right)~{\approx}~\frac{1}{24}\text{,}
$$

which is around $4\\%$.
which is around $4\%$.

Sect. 16.8 in the book runs through
the related, intriguing mathematics in great detail.
Expand Down
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