Revision as of 02:00, 24 March 2011

Bit Shifting : how i learned to stop worrying and love binary numbers

Here is how to deal with binary numbers when you are programming on an old computer (Basic V 2.0 on Commodore 64) or when you are configuring internal parameters on your arduino board. Thanks to Mr. Stock who made this nightmare look nearly simple.

What is << (bit shifting) ?

In the binary numeral system, everything looks like 0110010100010100111...
A bit shift consists in moving one or several digits in a line of 0110010100010100111...

Examples

1 << 3

1 = 0001 in the binary numeral system
1 << 3 means we are gonna move the value 1, to the left <<, 3 times.
1 << 3 : 0001  ->  0010  ->  0100  ->  1000   
               1st move  2nd move  3rd move

1 << 3 = 1000 and 1000 in the binary numeral system = 8

7 << 5

7 = 00000111
7 << 5 : 0000 0111  ->  0000 1110  ->  0001 1100  ->  0011 1000  ->  0111 0000  ->  1110 0000 

7 << 5 = 1110000 in the binary numeral system = 224

@@ Line 1: / Line 1: @@
 __NOTOC__
 __NOEDITSECTION__
-==<span style="color:#00FF00">Bit Shifting : learning how to count like a machine</span>==
+==<span style="color:#00FF00">Bit Shifting : how i learned to stop worrying and love binary numbers</span>==
-The idea is to work with inputs and outputs of Arduino to make a Simon says kind of game.
+Here is how to deal with binary numbers when you are programming on an old computer (Basic V 2.0 on Commodore 64) or when you are configuring internal parameters on your arduino board. Thanks to Mr. Stock who made this nightmare look nearly simple.
 <br />
-==How does it work ?==
+==What is << (bit shifting) ?==
-====Technologies involved====
+In the binary numeral system, everything looks like 0110010100010100111... <br />
-[http://en.wikipedia.org/wiki/Arduino Arduino]
+A bit shift consists in moving one or several digits in a line of 0110010100010100111... <br />
-====Steps====
-#We need a board with a push button and a speaker.
-#The code uses two ''while'' loops, constantly checking if the button is pressed, for how long, and launching a timeout during the waiting loop, in order to play the sequence after 5 seconds of wait.
+====Examples====
 <br />
-==Source code==
+<< 3
+<pre>
+= 0001 in the binary numeral system
+<< 3 means we are gonna move the value 1, to the left <<, 3 times.
+<< 3 : 0001  ->  0010  ->  0100  ->  1000
+st move  2nd move  3rd move
-<source lang="C">
+<< 3 = 1000 and 1000 in the binary numeral system = 8
-const int buttonPin = 7;
+</pre>
-int buttonState = 0;
+<< 5
-int value1;
+<pre>
-int value2;
+= 00000111
-int interval;
+<< 5 : 0000 0111  ->  0000 1110  ->  0001 1100  ->  0011 1000  ->  0111 0000  ->  1110 0000
-int pattern[100];
-int i = 0;
-int j = 0;
-int wfp_start;
-void setup() {
+<< 5 = 1110000 in the binary numeral system = 224
-  // 9600 is the frequency that will be used by the monitor
+</pre>
-  Serial.begin(9600);
-  pinMode(buttonPin, INPUT);
-}
-void loop(){
+<br />
+=The best is yet to come=
-  while (1) {
+==The nibble==
+==Big endian Vs little endian==
-    // State : WAIT FOR PRESS
+==Logical operations==
-    wfp_start = millis();
+==Bits and modulo==
-    while (digitalRead(buttonPin) == LOW && (millis() - wfp_start < 5000 )) {
-      // Do nothing the button isn't pressed
-    }
-    // Act as a timeout. Above 5 sec, we exit the WAIT loop and PLAY
-    if ((millis() - wfp_start >= 5000 )) break;
-    // State : WAIT FOR RELEASE
-    value1 = millis();
-    while (digitalRead(buttonPin) == HIGH) {
-      // Play tone when the button is pressed
-      tone(8, 100, 5);
-    }
-    value2 = millis();
-    interval = value2 - value1;
-    pattern[i]= interval;
-    Serial.println(pattern[i]);
-    // This will be used to simplify the values stored in the array
-    if (pattern[i] < 100) pattern[i] = 100;
-    else if (pattern[i] > 99 && pattern [i] < 200) pattern[i] = 200;
-    else if (pattern[i] > 199 && pattern [i] < 300) pattern[i] = 300;
-    else pattern[i] = 400;
-    Serial.println(" pattern : ");
-    Serial.println(pattern[i]);
-    i++;
-  }
-    // State : PLAY
-    while (j < i) {
-      tone(8, 100, pattern[j]);
-      Serial.println("Pattern plays");
-      j++;
-    }
-}
-</source>