# Significance of the numbers used in the manual

i just bought the starter kit and am currently working my way through the examples in the book when i came across some numbers used in the manual that seems a little too specific.

For example, in project #3,the love-o-meter, i had to divide the sensor value by 1024.0, and the explanation for it was never given in the manual.

Furthermore, in project #4(which i'm currently at), the book states that i have to convert sensor readings from 0 - 1023, to a value between 0 to 255.Is the number 1024/1023 simply an arbitrary number/limit set by the sensor's manufacturers? Also, is they any significance or reason that analogueWrite only accepts positive values up to 255?

Thanks!

The range 0 - 1023 comes from the analog-to-digital converters (ADC) built-in to your Arduino. What they do is take a voltage reading (e.g. from your sensor) and compare it to the analog reference voltage (which is typically 5 volts, although it can be changed).

It converts that reading to a binary number. The ADCs on board a typical Arduino have 10 bits of precision. The maximum number you can represent with 10 binary bits is 1023. Therefore, a reading of 0V is converted to the number 0; a reading of 5V is converted to the number 1023; and so on (it handles all the in-between values too).

However, `analogWrite()` works quite differently. It's not actually producing a varying voltage on the output (i.e. it's not true digital-to-analog conversion). Instead, it's using Pulse Width Modulation (PWM) to do something similar.

That means it sends lots of 5V pulses on the output in quick succession. The 0 - 255 values you give it affect the duty cycle -- that is, how long each pulse is compared to the gaps between pulses. The longer the pulses are, the 'stronger' the signal is. This is very useful for applications such as controlling the brightness of an LED or the speed of a basic DC motor.

The PWM signal is controlled by timers built-in to the microcontroller. I suspect it's the capabilities of those timers which determine the input range for `analogWrite()`.

• It's the minimum of the timer capabilities. The 8-bit timers are naturally restricted to 8-bit PWM precision, but even the 16-bit timers are reduced to 8-bit precision for consistency's sake. – Ignacio Vazquez-Abrams May 24 '14 at 10:39

To clarify, analogRead() has a 10 bit range due to the arduino's Analog to Digital Converter, or ADC. 10 bits can store 1024 (2^10) different values; counting zero as a value gives the range 0-1023.

In arduino 0 is the reading when a pin is grounded, 1023 is the reading when an analog pin is connected to Vref, or 5v if there is nothing wired to Vref. The sensors provide a voltage somewhere between these values, but not the actual numbers your code gets.

analogWrite() accepts 8 bit numbers. That is 2^8 or 256 different values, called 0-255. It only simulates an analog voltage by pulsing a pin rapidly.

In short, the numbers are not arbitrary, but express the limits of the arduino chip's IO. They look random because they were written in decimal, but in binary they are very simple. If you are interested, you could look into replacing the decimal numbers in the code with hexadecimal numbers, which make their binary representations very obvious by way of 16 being 2^4.

More explanation: binary numbers are different than base 10 as you probably know. The meaning of those numbers is simple.

Start with 1 and double it. Keep doubling. You will soon hit 256 (computers start at 0 not 1, so you have to take that into account, 0-255 is 256 different values). Keep doubling and you will soon hit 1024 (0-1023).

So these numbers are not arbitrary, they are Base 10 (0-9 like you learned in school) representations of Binary Numbers, more specifically, the high limit a given length of binary digits can represent before having to add another digit.

1111111 is binary for 127, with 0 thats 128 different values those 7 digits can represent. To get to 255, you have to add a digit for 8 total digits, 11111111 = 255. 9 digits or 111111111 = 511 and ten digits or 1111111111 = 1023.