Mandelbrot set is one of the most famous fractal images. The following Forth program is used to plot the Mandelbrot set.

Representation of Fixed-Point Numbers

Fixed-point numbers in Qint.frac format are used for computation. int is the number of bits for the integer part (including the sign bit, if any), and frac is the number of bits for the fractional part. In the following program, the width of the fixed-point number is 16 bits (the same as a single-precision integer in Forth), i.e., int+frac=16.

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cwt provides an Arch Linux image for the VisionFive 2 RISC-V single-board computer. In this image, U-Boot uses the mainline version, which, compared to the version provided by StarFive, cannot recognize the 16GB Optane M10 (MEMPEK1J016GAL) at boot. Here is the method to boot Arch Linux with 16GB Optane on the VisionFive 2 using the U-Boot provided by StarFive.

Preparation

Download the image ArchLinux-VF2_6.12_v6.0.0-cwt25.img.zst here，burn it to a micro SD card.

Download the SPL (u-boot-spl.bin.normal.out) and U-Boot (visionfive2_fw_payload.img) provided by StarFive here.

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It is often necessary to calibrate the shutter speed when repairing cameras. The table below provides the upper and lower limits of exposure time calculated according to the method specified in ISO 516:2019 “Camera shutters — Timing — General definition and mechanical shutter measurements”.

Nominal exposure time values/s	Calculated exposure time values/s	Calculated exposure time values/ms	Upper admissible values of exposure times/ms	Lower admissible values of exposure times/ms
8	8	8000	9850	6500
4	4	4000	4920	3250
2	2	2000	2460	1625
1	1	1000	1231	812
1/2	1/2	500	616	406
1/4	1/4	250	308	203
1/8	1/8	125	154	102
1/15	1/16	62.5	76.9	50.8
1/30	1/32	31.3	38.5	25.4
1/60	1/64	15.6	19.2	12.7
1/125	1/128	7.81	9.62	6.35
1/250	1/256	3.91	5.34	2.86
1/500	1/512	1.95	2.67	1.43
1/1000	1/1024	0.98	1.33	0.71
1/2000	1/2048	0.49	0.67	0.36

Excel spreadsheet can be downloaded here.

The program of the RP2040 is stored in the SPI Flash, and during runtime, the program in the Flash is randomly read into the internal cache for execution. This does not pose a problem when working in single-core mode. However, in multicore mode, if one core is executing the program while another core is writing to the Flash (for example, using the littlefs file system to manage the remaining space in the SPI Flash that does not store the program), it may cause simultaneous reading and writing of the Flash, leading to the program on one or both cores hanging.

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The decibel (dB) is widely used in electronics to describe ratios. Many people find this logarithmic unit difficult to understand, but in fact, it was designed for mental calculation and should not be perceived as overly complicated.

dB is suitable for situations where the dynamic range is large but the requirement for significant digits is not high. For example, whether the exact value of ripple rejection ratio is ten thousand times (80 dB) or fifteen thousand times (83 dB) is not particularly important; it is sufficient to know that it is not one thousand times (60 dB).

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The most common marking system for chip resistors is the three/four-digit marking system, where the first two/three digits are the significant figures, and the last digit is the order of magnitude (in ohms, indicating the number of zeros added after the significant figures). For resistors less than 10 Ω or 100 Ω, the decimal point is represented by the letter R. For example:

Marking 1	Marking 2	Value
681	6800	680 Ω
914	9103	910 kΩ
R01	010, R010	10 mΩ
6R8	6R80	6.8 Ω

Due to the limited printable area on 0603 chip resistors (0402 and smaller packages generally have no markings), some E96 (1%) 0603 chip resistors use the two-digit plus one-letter marking method described below to save one character. This method is also known as the EIA-96 SMD Resistor Code.

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Problem

Calculate

\[ \begin{align*} I(t)= & A \cos\omega t, \\ Q(t)= & A \sin \omega t \\ \end{align*} \]

from acquired signal

\[ \begin{align*} I_0(t)= & A \alpha \cos \omega t, \\ Q_0(t)= & A \sin(\omega t+\psi). \end{align*} \]

Equations

From

\[\sin(\omega t + \psi)=\sin \omega t \cos\psi+\cos \omega t \sin\psi\]

we have

\[\begin{pmatrix}I_0(t) \\ Q_0(t)\end{pmatrix} = \begin{pmatrix}\alpha & 0 \\ \sin \psi & \cos \psi\end{pmatrix} \begin{pmatrix}I(t) \\ Q(t)\end{pmatrix} ; \]

I(t) and Q(t) can be obtained by matrix inversion:

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EEPROM Card and Backplane

EEPROM Card

For EEPROM cards, firmware provided on this website arranges adjacent blocks on the same EEPROM chip, with block numbers ordered according to EEPROM addresses.

The EEPROM card card uses a USB 3.0 Type-A interface, where the power contacts are compatible with standard USB interfaces, and the signal contacts are used for I2C interface and addressing:

SOCKET connects to EEPROM address line A1：

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Working at 20MHz and 22.1184MHz

Tests have shown that My4TH can operate stably at 20MHz (using the 10MHz ROM image file provided by the original author at baud rate 9600) by increasing Vcc to 5.2V with 74HC series logic circuits and AM27H256-45/35DC.

This configuation can work at 22.1184MHz with Vcc=5.4V:

U2 U3	U4	U9	U15	U16	Others
74F161A(TI)/ 74AC161(TI)	74LVC541A(TI)	74ACT08/ 74LVC08	AM27H256-45/35DC (needs to be selected)	IS61C256AL-12T(L)I/ CY7C199(L)-15ZC	74HC series

Higher baud rate

By adjusting the delays in serial subroutines, the system can operate at 14400 baud above 16MHz and 19200 at 22.1184MHz.

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In the 1960s and 1970s, Broadcast radio receiver was an essential tool for debugging computer memory. Users could use an ordinary broadcast radio to monitor the electromagnetic radiation emitted by the computer, confirming the operational status of magnetic core memory and the bus. Users quickly discovered that this phenomenon could be used to play music (e.g. here and here).

While My4TH utilizes modern EPROM and SRAM, its bus still generates some electromagnetic radiation. Experiments have shown that a regular AM radio can pick up the electromagnetic radiation caused by status changes in the bus.

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