Microchip Technology

ATMEGA168P-20PU - 8-Bit AVR MCU 20MHz 16KB Flash | Microchip

Артикул: ATMEGA168P-20PU ✓ Активен
В наличии Отправка в течение 1–3 рабочих дней
2.7 V to 5.5 V Vdss 28-PDIP (0.300 inch, 7.62 mm) Package 20 MHz Speed 16 KB (8K x 16) Memory
От $2.05 USD / шт.
MOQ: 1 |
Цена обновлена: 2026-09-16
Оптовые цены
Кол-во Цена за ед. Итого
1 $3.2 $3,20
10 $2.88 $28,80
100 $2.56 $256,00
500 $2.3 $1.150,00
1.000 $2.05 $2.050,00
ℹ️ Все цены указаны в USD

ATMEGA168P-20PU Обзор

The Microchip Technology (Atmel) ATMEGA168P-20PU is a picoPower 8-bit AVR RISC microcontroller delivering 20 MIPS at 20 MHz, with 16KB ISP flash memory, 1KB SRAM, 512B EEPROM, and 23 general-purpose I/O lines in a 28-pin PDIP package rated for industrial temperatures.

An 8-bit AVR microcontroller is a Harvard-architecture RISC processor that executes most instructions in a single clock cycle. Within the power-management hierarchy, it integrates the CPU, program memory, data memory, timers, communication peripherals, and analog-to-digital converter on a single chip, making it a complete embedded control solution without external components. The ATmega168P family sits between the smaller ATmega48 and the larger ATmega328 in the AVR flash microcontroller lineup.

Key features include 16KB of in-system-programmable flash with read-while-write support, a 10-bit ADC with up to 8 multiplexed channels (TQFP/QFN packages; 6 channels on PDIP), three flexible timer/counters with compare modes, and debugWIRE on-chip debugging. The picoPower technology enables low-power sleep modes for battery-operated designs, and supply voltage spans 2.7V to 5.5V.

Architecturally, the AVR core uses 32 general-purpose working registers directly connected to the ALU, allowing one-cycle execution of most instructions - 133 powerful instructions in total. On-chip peripherals include USART, SPI, and two-wire (I2C-compatible) serial interfaces, plus a watchdog timer, brown-out detection, and power-on reset.

Typical applications include hobbyist and Arduino-compatible boards, industrial sensor nodes, consumer appliance control, and low-power battery products where the through-hole PDIP package simplifies prototyping and rework.

A key design consideration is clock selection: full 20 MHz operation requires 4.5V-5.5V; at 2.7V the maximum safe frequency is lower, so set fuse bits accordingly.

This page synthesizes distributor pricing, pin-compatible drop-in alternatives, and practical design notes not found in the manufacturer datasheet.

Аналоги без доработки для ATMEGA168P-20PU — тот же корпус, pin-to-pin совместимость. Компоненты в других корпусах, требующие переработки PCB, исключены.

Варианты в этой серии

Модели той же серии, совместимые без доработки с ATMEGA168P-20PU (тот же форм-фактор и посадочное место) — отличается по Working Registers, Package, Instructions, Timers/Counters, EEPROM.

Microchip Technology
Working Registers: 32 x 8-bit
Сравнить с ATMEGA168P-20PU →
Microchip Technology
Working Registers: 32
Package: 28-PDIP (0.300 in, 7.62 mm), through-hole
Timers/Counters: 3 (with compare and PWM modes)
Сравнить с ATMEGA168P-20PU →
Microchip Technology
Working Registers: 32 general purpose
Package: 28-PDIP
Instructions: 131 instructions, most single-cycle
Сравнить с ATMEGA168P-20PU →
Microchip Technology
Working Registers: 32 x 8 general purpose
Package: 28-PDIP
Instructions: 130 instructions, most single-cycle
Сравнить с ATMEGA168P-20PU →

Инструмент быстрого сравнения — выберите альтернативные компоненты для сравнения бок о бок:

ATMEGA168PA-PU

✅ Прямая замена
Microchip Technology
📦 28-PDIP
8-bit AVR RISC · 16 KB (8K x 16) · 1 KB · 512 B · 20 MHz · 2.7 V to 5.5 V · 23 · 32

✓ В наличии

$1.86 / шт.

Открыть даташит →

ATMEGA168A-PU

✅ Прямая замена
📦 28-PDIP
same family/process migration, identical memory (16KB/1KB/512B) and 20 MHz speed; minor sleep-mode current differences

📋 Справочный аналог (нет в каталоге)

ATMEGA168-20PU

✅ Прямая замена
Microchip Technology
📦 28-PDIP
AVR 8-bit RISC · 8-Bit · 20 MHz · 16 KB (8K x 16) · 512 B · 1 KB · 2.7 V to 5.5 V · 23

✓ В наличии

$3.78 / шт.

Открыть даташит →

ATMEGA328P-PU

✅ Прямая замена ⚠️ Характеристики не проверены
Microchip Technology
📦 28-PDIP
8-bit AVR RISC · 32 KB (16K x 16) · 1 KB · 2 KB · 20 MHz · 16 MHz · 4.5 V to 5.5 V · 23

✓ В наличии

Уточнить цену

Открыть даташит →

ATMEGA8A-PU

✅ Прямая замена ⚠️ Характеристики не проверены
Microchip Technology
📦 28-PDIP
8-bit AVR RISC · 16 MHz · 8 KB (4K x 16) ISP · 1 KB · 512 B · 4.5 V to 5.5 V · 23 · 16 MIPS at 16 MHz

✓ В наличии

$1.86 / шт.

Открыть даташит →

ATMEGA168P-20PU Максимальные параметры и электрические характеристики

Core Processor AVR 8-bit RISC
Core Size 8-Bit
Максимальная тактовая частота 20 MHz
Flash Memory 16 KB (8K x 16)
SRAM 1 KB
EEPROM 512 B
Supply Voltage Range 2.7 V to 5.5 V
Number of I/O 23
ADC Resolution 10-bit
ADC Channels 8 (6 on PDIP package)
Timers/Counters 3 (two 8-bit, one 16-bit)
Communication Interfaces USART, SPI, I2C (TWI)
Instructions 133, most single-cycle
Рабочая температура -40C to +85C (industrial)
Корпус 28-PDIP (0.300 inch, 7.62 mm)
Тип монтажа Through Hole
Programmability ISP (In-System Programmable), debugWIRE
Статус RoHS Compliant (GREEN)
Статус жизненного цикла Active (newer device ATMEGA168PA available)

Конфигурация выводов ATMEGA168P-20PU

DIP-28 Package Pinout Diagram DIP-28 28-pin dual inline, 7.62mm pitch, JEDEC MS-001. 1 28 2 27 3 26 4 25 5 24 6 23 7 22 8 21 9 20 10 19 11 18 12 17 13 16 14 15 DIP-28
Контакт 1 PC6 (RESET) — Reset input (active low); also PC6 I/O if RSTDISBL fuse programmed
Контакт 2 PD0 (RXD) — Port D bit 0; USART receive data
Контакт 3 PD1 (TXD) — Port D bit 1; USART transmit data
Контакт 4 PD2 (INT0) — Port D bit 2; external interrupt 0
Контакт 5 PD3 (INT1/OC2B) — Port D bit 3; external interrupt 1 / Timer2 PWM output B
Контакт 6 PD4 (T0/XCK) — Port D bit 4; Timer0 external clock / USART external clock
Контакт 7 VCC — Digital supply voltage (2.7V to 5.5V)
Контакт 8 GND — Ground
Контакт 9 PB6 (XTAL1/TOSC1) — Port D... Port B bit 6; crystal oscillator input / Timer oscillator
Контакт 10 PB7 (XTAL2/TOSC2) — Port B bit 7; crystal oscillator output / Timer oscillator
Контакт 11 PD5 (OC0B/T1) — Port D bit 5; Timer0 PWM output B / Timer1 external clock
Контакт 12 PD6 (OC0A/AIN0) — Port D bit 6; Timer0 PWM output A / analog comparator positive input
Контакт 13 PD7 (AIN1) — Port D bit 7; analog comparator negative input
Контакт 14 PB0 (ICP1/CLKO) — Port B bit 0; Timer1 input capture / system clock output
Контакт 15 PB1 (OC1A) — Port B bit 1; Timer1 PWM output A
Контакт 16 PB2 (OC1B/SS) — Port B bit 2; Timer1 PWM output B / SPI slave select
Контакт 17 PB3 (MOSI/OC2A) — Port B bit 3; SPI master output / Timer2 PWM output A
Контакт 18 PB4 (MISO) — Port B bit 4; SPI master input
Контакт 19 PB5 (SCK) — Port B bit 5; SPI serial clock
Контакт 20 AVCC — ADC supply voltage; connect to VCC through low-pass filter or directly
Контакт 21 AREF — ADC analog reference voltage
Контакт 22 GND — Ground (ADC ground reference)
Контакт 23 PC0 (ADC0) — Port C bit 0; ADC channel 0
Контакт 24 PC1 (ADC1) — Port C bit 1; ADC channel 1
Контакт 25 PC2 (ADC2) — Port C bit 2; ADC channel 2
Контакт 26 PC3 (ADC3) — Port C bit 3; ADC channel 3
Контакт 27 PC4 (ADC4/SDA) — Port C bit 4; ADC channel 4 / I2C data
Контакт 28 PC5 (ADC5/SCL) — Port C bit 5; ADC channel 5 / I2C clock

Типичное применение

ATMEGA168P-20PU подходит для 6 применениеs: Arduino-Compatible Hobbyist and Maker Boards, Industrial Sensor Nodes and Data Loggers, Low-Power Battery-Operated Devices, Consumer Appliance and Home Control, Prototyping, Education, and Legacy Through-Hole Systems, Motor Control and PWM Actuation.

🧩

Arduino-Compatible Hobbyist and Maker Boards

The ATMEGA168P-20PU is a natural fit for Arduino-compatible through-hole boards because it shares the exact DIP-28 pinout, fuse map, and bootloader workflow of the Arduino Uno's ATmega328P. Its 16KB ISP flash accepts the standard optiboot bootloader, and the 20 MHz clock delivers 20 MIPS for typical sketch workloads. The removable PDIP package lets makers swap or reprogram chips in a ZIF socket without desoldering, a key advantage over QFN/TQFP parts. Designers should budget sketch size against the 16KB flash (roughly half the Uno's 32KB) and reserve 512B EEPROM for calibration or user settings.

🏭

Industrial Sensor Nodes and Data Loggers

In industrial monitoring, the ATMEGA168P-20PU combines a 10-bit ADC (6 channels available on the PDIP pinout), the two-wire I2C interface for digital sensors, and picoPower sleep modes that cut consumption to microamp levels between samples. Supply operation from 2.7V to 5.5V allows direct powering from 3.3V or 5V rails common in PLC-adjacent hardware, and the -40C to +85C industrial rating covers unconditioned enclosures. A typical node sleeps between ADC conversions of thermistors or potentiometers, wakes via timer or external interrupt, and streams readings over USART or SPI; brown-out detection and the watchdog timer safeguard long-duration deployments.

🔋

Low-Power Battery-Operated Devices

PicoPower technology makes the ATMEGA168P-20PU suitable for battery products that spend most of their life asleep: power-down sleep modes drop current to the microamp range while the asynchronous timer or pin-change interrupt provides wake sources. Designers clock the chip from the internal 8 MHz RC oscillator or a 32.768 kHz watch crystal to minimize active energy, and the wide 2.7V-5.5V supply range permits direct use of 3xAA cells or a single lithium cell through a small regulator. The watchdog timer supports periodic wake scheduling, and debugWIRE enables single-wire in-canvas debugging without sacrificing port pins.

🏠

Consumer Appliance and Home Control

Appliance interfaces, thermostats, and small home-automation controllers benefit from the ATMEGA168P-20PU's blend of through-hole robustness and integrated peripherals. The three timers with compare modes generate PWM for heater, fan, or lamp dimming control, while USART and SPI link to displays or wireless modules. The 23 I/O lines directly drive keys, relays (via driver transistors), and LEDs, and the internal RC oscillator option removes the crystal from cost-sensitive boards. RoHS-compliant GREEN packaging and the industrial temperature range simplify qualification for globally shipped consumer goods.

🔧

Prototyping, Education, and Legacy Through-Hole Systems

The 0.3-inch PDIP package is the decisive factor in education labs, breadboard prototyping, and servicing of legacy through-hole equipment. Students and engineers can insert the ATMEGA168P-20PU directly into breadboards or ZIF sockets, program it via SPI with standard AVR ISP tools, and replace it at pennies if damaged. In repair scenarios, the pin-compatibility across the ATmega8/168/328 DIP-28 family lets technicians substitute whatever family member is procurable. The AVR instruction set, shared across the family and supported by avr-gcc and Microchip Studio, keeps course material and legacy codebases valid for years.

⚙️

Motor Control and PWM Actuation

The ATMEGA168P-20PU's three timer/counters - two 8-bit and one 16-bit - each support compare-match PWM outputs, enabling simultaneous multi-channel control of DC motors, servos, and LED drivers. High-speed PWM modes allow carrier frequencies above the audible range, and the 16-bit timer provides precise servo pulse timing. Interrupt-driven quadrature decoding on the pin-change interrupt ports supports closed-loop speed control with optical encoders, while the SPI interface connects to dedicated motor-driver configurations. The 20 MIPS core leaves ample headroom for PI control loops running at kilohertz rates.

What are the key specifications of ATMEGA168P-20PU?
The ATMEGA168P-20PU is an 8-bit AVR RISC microcontroller from Microchip (originally Atmel) with 16KB ISP flash, 1KB SRAM, 512B EEPROM, 23 I/O lines, and a 20 MHz maximum clock (20 MIPS). It operates from 2.7V to 5.5V, integrates a 10-bit ADC, three timers, and USART/SPI/I2C interfaces, and is housed in a 28-pin PDIP package for industrial temperature ranges.
What is the price of ATMEGA168P-20PU?
The ATMEGA168P-20PU typically sells for around $3.20 at quantity 1, dropping to roughly $2.05 at 1000 units, based on pricing compiled from 14 distributors on Octopart. Pricing varies by distributor and stock position, so compare live quotes before ordering. All prices on this page are as of 2026-09-16 and should be verified at checkout since MCU market pricing fluctuates with supply conditions.
Where to buy ATMEGA168P-20PU online?
You can buy the ATMEGA168P-20PU from XAIPART directly on this page, or from major distributors including DigiKey, Mouser, and the 14 distributors aggregated by Octopart. DigiKey lists it with same-day shipping in stock. For production volumes, MicrochipDirect also offers factory-direct ordering of this PDIP package with volume pricing and reel or tube options.
What is the best drop-in replacement for ATMEGA168P-20PU?
The best drop-in replacement is the ATMEGA168PA-PU, a pin-compatible 28-PDIP device with identical 16KB flash, 20 MHz speed, and peripherals, offering slightly lower power consumption. Microchip itself notes a newer device is available (ATMEGA168PA). ATMEGA168A-PU and ATMEGA168-20PU are also pin-to-pin DIP-28 substitutes. All accept the same code base with no PCB changes.
Is ATMEGA328P-PU compatible with ATMEGA168P-20PU?
Yes, the ATMEGA328P-PU is pin-compatible with the ATMEGA168P-20PU in the 28-pin PDIP package and runs the same AVR core at 20 MHz. The main difference is memory: the ATMEGA328P has 32KB flash and 2KB SRAM versus 16KB and 1KB, so code compiled for the ATmega168 fits, but the reverse is not true. Verify fuse settings and bootloader differences before swapping.
What is the difference between ATMEGA168P and ATMEGA168A?
The ATMEGA168P is a picoPower variant of the ATmega168 family, while the ATMEGA168A is a later process migration with the same 16KB flash, 1KB SRAM, and peripherals. Both are pin-to-pin compatible in 28-PDIP and interchangeable in most designs. The P version emphasizes low-power sleep modes; check the current datasheet tables for exact active and sleep current figures for your voltage and frequency.
Can I use ATMEGA168P-20PU at 3.3V?
Yes, the ATMEGA168P-20PU operates from 2.7V to 5.5V, so 3.3V operation is supported. However, the -20 speed grade of 20 MHz is guaranteed only at the top of the voltage range (4.5V-5.5V); at 3.3V the safe maximum frequency is lower (approximately 13.3 MHz per AVR frequency-versus-voltage derating). Alternatively choose the ATMEGA168P-15 or -8 speed grade for low-voltage designs.
Does the ATMEGA168P-20PU support Arduino development?
Yes, the ATMEGA168P-20PU works with Arduino IDE using the ATmega168 board definition. It is the predecessor of the ATmega328P used on the Arduino Uno, sharing the same DIP-28 pinout, peripherals, and programming workflow. You can program it in-system via SPI with an AVR ISP programmer or via a serial bootloader; note the flash is 16KB, roughly half of the Uno's, limiting sketch size.
Where can I download the ATMEGA168P-20PU datasheet PDF?
Download the ATMEGA168P-20PU datasheet from the official Microchip product page at microchip.com/en-us/product/ATmega168P, which hosts the complete 8-bit AVR with 4/8/16/32K Bytes In-System Programmable Flash datasheet. The document covers the full ATmega48A/PA/88A/PA/168A/PA/168P family, so pinout, registers, and electrical characteristics apply to the -20PU variant.
Where can I find the ATMEGA168P-20PU pinout for the 28-pin DIP package?
The ATMEGA168P-20PU pinout is shown on this page under the pinout diagram: pin 1 is PC6/RESET, pins 2-6 and 11-13 are port D (PD0-PD7), pins 7-8 are VCC/GND, pins 9-10 are XTAL1/XTAL2 (PB6/PB7), pins 14-19 are port B, pin 20 is AVCC, pin 21 AREF, pin 22 GND, and pins 23-28 are port C (ADC inputs with I2C on PC4/PC5).
Is ATMEGA168P-20PU the same as ATMEGA168PA-PU?
No, they are not identical parts, but the ATMEGA168PA-PU is functionally equivalent and pin-compatible. The PA is a die shrink/renewal of the P with the same 16KB flash, 1KB SRAM, 20 MHz rating, and 28-PDIP package, typically with improved efficiency. Microchip officially lists ATMEGA168PA as the newer device for ATMEGA168P, making it the recommended substitution path for new designs.
When should I choose ATMEGA168P-20PU over ATMEGA328P-PU?
Choose the ATMEGA168P-20PU when your firmware fits in 16KB flash and you want the lowest cost in the DIP-28 AVR family. Choose the ATMEGA328P-PU when you need 32KB flash and 2KB SRAM for larger Arduino sketches or OTA-update headroom. Both are pin-compatible, so designing the PCB around the 28-pin footprint lets you swap between them freely.
What is the lead time and stock status for ATMEGA168P-20PU?
The ATMEGA168P-20PU is an active product; DigiKey lists it with same-day shipping when in stock, and Octopart aggregates availability from 14 distributors. Because it is a through-hole legacy-oriented package, some distributors carry limited depth, so check live stock before committing to production schedules. For volume requirements, request factory lead times via MicrochipDirect.
What Microchip (or other brand) equivalent exists for ATMEGA168P-20PU?
The primary equivalents are Microchip's own family members: ATMEGA168PA-PU (newer picoPower revision), ATMEGA168A-PU, and ATMEGA168-20PU, all pin-compatible 28-PDIP devices. A true cross-brand pin-to-pin equivalent in PDIP-28 is not available because AVR pinout and instruction set are proprietary; Microchip PIC or ST parts would require PCB and firmware redesign, so they are not drop-in alternatives.
Is the ATMEGA168P-20PU RoHS compliant and lead-free?
Yes, the ATMEGA168P-20PU is RoHS compliant; distributor and datasheet listings mark it GREEN and the PU suffix denotes lead-free 28-PDIP packaging in an industrial temperature grade (-40C to +85C). Microchip maintains full RoHS and REACH declarations on its product pages, and the device is suitable for lead-free reflow and soldering processes in compliance with current environmental regulations.

Справочные инженерные данные для ATMEGA168P-20PU — сравнение, рекомендации по проектированию и информация о соответствии.

Руководство по выбору

Choose the ATMEGA168P-20PU when you need a through-hole, 20 MIPS AVR with 16KB flash at the lowest cost, especially for prototyping, education, or battery products that exploit picoPower sleep modes. Choose the ATMEGA168PA-PU when starting a new design - it is the same device revised, carries the longest supply commitment, and reaches slightly lower voltage (1.8V). Choose ATMEGA168A-PU or ATMEGA168-20PU when low-power sleep modes are irrelevant and price or availability favors the older die. Step up to ATMEGA328P-PU (same DIP-28 pinout, 32KB flash, 2KB SRAM) when firmware outgrows 16KB or you want Arduino Uno compatibility; drop to ATMEGA8A-PU only when code fits 8KB and reduced peripherals suffice. All share one PCB footprint, so layout once and swap freely.

Сравнение с аналогами

Параметр Этот товар ATMEGA168PA-PU ATMEGA168A-PU ATMEGA168-20PU ATMEGA328P-PU
Package 28-PDIP 28-PDIP - same 28-PDIP - same 28-PDIP - same 28-PDIP - same
Brand Microchip Technology (Atmel) Microchip Technology Microchip Technology Microchip Technology Microchip Technology
Flash Memory 16 KB 16 KB 16 KB 16 KB 32 KB
SRAM 1 KB 1 KB 1 KB 1 KB 2 KB
EEPROM 512 B 512 B 512 B 512 B 1 KB
Max Clock Frequency 20 MHz 20 MHz 20 MHz 20 MHz 20 MHz
Supply Voltage 2.7 V to 5.5 V 1.8 V to 5.5 V 2.7 V to 5.5 V 2.7 V to 5.5 V 1.8 V to 5.5 V
picoPower Low-Power Technology Yes Yes No No Yes
Lifecycle Position Active (successor ATMEGA168PA designated) Active - newest revision Active Active (older die) Active - most popular AVR

Ключевые отличия

  • picoPower low-power technology (против ATMEGA168A-PU)
  • Designated successor availability (против ATMEGA168-20PU)
  • Cost efficiency versus memory headroom (против ATMEGA328P-PU)

Заметки по проектированию

Match clock speed to supply voltage: the -20 speed grade (20 MHz) is guaranteed only at 4.5V-5.5V per AVR frequency-versus-voltage derating curves. At 3.3V, keep the system clock at or below roughly 13 MHz (typically a 12 MHz crystal or the internal 8 MHz RC oscillator) to stay within the safe operating region. Decouple VCC and AVCC with 100 nF ceramic capacitors placed within 5 mm of the pins, and tie AVCC to VCC through a 10 uH/10 nF low-pass filter when ADC accuracy matters.

On the PDIP footprint, place the 100 nF decoupling capacitors on the component side directly across pins 7-8 (VCC-GND) and near pin 20 (AVCC). Keep the AREF trace short and decouple it with 100 nF to ground; never connect an external reference without this capacitor or ADC readings will be noisy. For ISP programming, route MOSI/PB3, MISO/PB4, SCK/PB5, and RESET/PC6 to a standard 2x3 100-mil header so AVR ISP and debugWIRE tools connect without rework.

Three frequent mistakes: (1) programming RSTDISBL fuse disables the RESET pin permanently, effectively bricking in-circuit reprogramming - avoid it unless high-voltage parallel programming is available; (2) setting CKDIV8 and clock fuses incorrectly for a 20 MHz crystal can leave the chip running at 2.5 MHz or with no clock at all; (3) forgetting that only 6 ADC channels are bonded out on the PDIP (ADC6/ADC7 exist only on TQFP/QFN) - do not write firmware that samples channels 6-7. Verify all fuse settings in AVR Fuse Calculator before flashing production units.

When driving long wires or cables from port pins, add 33-100 ohm series resistors to limit edge currents and reduce ringing, and keep the 20 MHz crystal within 10 mm of pins 9-10 with appropriate load capacitors (typically 18-22 pF; confirm with the crystal manufacturer's CL specification). For switching loads such as relays, always use a transistor driver with a flyback diode rather than driving directly from an I/O pin, which is limited to the absolute maximum 40 mA per pin.

Информация о соответствии

RoHS
Compliant
REACH
Unknown
AEC-Q100
Not Applicable
Без свинца
Yes
Без галогенов
Yes
Конфликтные минералы
Unknown

Distributor listings mark ATMEGA168P-20PU as GREEN industrial-temp PDIP, indicating RoHS compliance and lead-free/halogen-free construction. REACH and conflict-minerals declarations available from Microchip compliance portal.

Данные проверены: 2026-09-16 — данные проверены и курируются командой компонентной инженерии XAIPART

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Связанные компоненты & термины

Microchip Technology Atmel ATMEGA168P-20PU ATMEGA168PA-PU ATMEGA328P-PU ATMEGA168A-PU AVR 8-bit microcontroller RISC picoPower PDIP-28 ISP (In-System Programming) debugWIRE RoHS Arduino 10-bit ADC SPI I2C (TWI) USART embedded systems
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