user-1: I am designing 8*8 reed switch matrix which will be connected to Arduino. I am using Arduino Duemilanove. I have completed the matrix portion but don't know how to connect and where to connect the other elements.

I decided to use the following items:

Arduino (Duemilanove)
64x Reed Switch 
64x Diode (1N4148)
20x Resistors (10K)
1x 74HC595 
1x 74HC165 

I don't know where to place the Resistors and shift Registers and connection from shift registers to arduino. I need help in the circuit diagram. Please help me out with the circuit diagram.
Reference: https://mtifall10.wordpress.com/2010/12/10/magnetic-sensing-chessboard/

user59821: Use 16 digital i/o pins on the Arduino. The ones connected to a-h should be configured as OUTPUT pins. The ones connected to 1-8 should be configured as INPUT pins. Start with all of the outputs (a-h) low. 
You check for a closed switch at the lower left corner by making the output pin connected to 'a' HIGH then look at the value of the input pin connected to '1'. If it's high then that switch is closed. If it's low then that switch is open.
While the 'a' output is HIGH you can check the rest of the left column by looking at inputs '2' through '8'.
I don't see any need for the resistors or shift registers, but maybe your teacher had something in mind.
EDIT: I see that by using the shift registers you need only one INPUT pin and one OUTPUT pin on the Arduino. I'll leave that for you to figure out as I think I've given enough to get you started.

user28784: This answer is based on a previous version of the question

Not necessarily. You can use the internal pullups of the arduino if you're willing to accept that reading a "1" means that no piece is there and reading a "0" means a piece is there.
Connect each wire up to a pin on the arduino. If you do it wisely, step 3 becomes fairly easy.
You need to configure the pins connected to the letter wires as inputs with their pullups enabled. Set the number pins to inputs as well, but without the pullup enabled so that they are floating. The number pins will be each set as an output in sequence with the value being low (non-active number pins are set back to inputs). As you do so, you can read the pins on the letter wires and build a picture of the board.

Example
This is how I would do it just taking a naive stab at it. I'm sure there are more effective ways to do this.
Wiring:

Configure the outputs and inputs in setup:
pinMode(2, INPUT_PULLUP);
pinMode(3, INPUT_PULLUP);
pinMode(4, INPUT_PULLUP);
pinMode(5, INPUT_PULLUP);
pinMode(6, INPUT_PULLUP);
pinMode(7, INPUT_PULLUP);
pinMode(8, INPUT_PULLUP);
pinMode(9, INPUT_PULLUP);
pinMode(10, INPUT);
pinMode(11, INPUT);
pinMode(12, INPUT);
pinMode(13, INPUT);
pinMode(14, INPUT); //A0
pinMode(15, INPUT); //A1
pinMode(16, INPUT); //A2
pinMode(17, INPUT); //A3
pinMode(18, INPUT); //A4

Make a function to scan the rows into an array of bytes:
void scan_rows(uint8_t *rows)
{
    uint8_t i, j;

    for (i = 0; i < 8; i++)
    {
        if (i)
        {
            pinMode(i+9, INPUT);
        }
        pinMode(i+10, OUTPUT);
        digitalWrite(i+10, LOW);
        for (j = 2; j <= 9; j++)
        {
            rows[i] <<= 1;
            if (digitalRead(j))
                rows[i] |= 1;
        }
    }
    pinMode(18, INPUT);
}

Now, just call that function with a pointer to an array with 8 bytes in it whenever you need to scan the board. Each byte in the array represents one of the rows and each bit represents a column.
[moderator note: This answer appears in this thread as a result of a merge]

-1: <p>I am designing 8*8 reed switch matrix which will be connected to Arduino. I am using Arduino Duemilanove. I have completed the matrix portion but don't know how to connect and where to connect the other elements.
<img src="https://i.stack.imgur.com/76A84.jpg" alt="My Matrix circuit"></p>

<p>I decided to use the following items:</p>

<ul>
<li>Arduino (Duemilanove)</li>
<li>64x Reed Switch </li>
<li>64x Diode (1N4148)</li>
<li>20x Resistors (10K)</li>
<li>1x 74HC595 </li>
<li>1x 74HC165 </li>
</ul>

<p>I don't know where to place the Resistors and shift Registers and connection from shift registers to arduino. I need help in the circuit diagram. Please help me out with the circuit diagram.</p>

<p><strong>Reference:</strong> <a href="https://mtifall10.wordpress.com/2010/12/10/magnetic-sensing-chessboard/" rel="nofollow noreferrer">https://mtifall10.wordpress.com/2010/12/10/magnetic-sensing-chessboard/</a></p>
 59821: <p>Use 16 digital i/o pins on the Arduino. The ones connected to a-h should be configured as OUTPUT pins. The ones connected to 1-8 should be configured as INPUT pins. Start with all of the outputs (a-h) low. </p>

<p>You check for a closed switch at the lower left corner by making the output pin connected to 'a' HIGH then look at the value of the input pin connected to '1'. If it's high then that switch is closed. If it's low then that switch is open.</p>

<p>While the 'a' output is HIGH you can check the rest of the left column by looking at inputs '2' through '8'.</p>

<p>I don't see any need for the resistors or shift registers, but maybe your teacher had something in mind.</p>

<p>EDIT: I see that by using the shift registers you need only one INPUT pin and one OUTPUT pin on the Arduino. I'll leave that for you to figure out as I think I've given enough to get you started.</p>
 28784: <p><strong>This answer is based on a previous version of the question</strong></p>

<ol>
<li><p>Not necessarily. You can use the internal pullups of the arduino if you're willing to accept that reading a "1" means that no piece is there and reading a "0" means a piece is there.</p></li>
<li><p>Connect each wire up to a pin on the arduino. If you do it wisely, step 3 becomes fairly easy.</p></li>
<li><p>You need to configure the pins connected to the letter wires as inputs with their pullups enabled. Set the number pins to inputs as well, but without the pullup enabled so that they are floating. The number pins will be each set as an output in sequence with the value being low (non-active number pins are set back to inputs). As you do so, you can read the pins on the letter wires and build a picture of the board.</p></li>
</ol>

<p><strong>Example</strong></p>

<p>This is how I would do it just taking a naive stab at it. I'm sure there are more effective ways to do this.</p>

<p>Wiring:</p>

<p><a href="https://i.stack.imgur.com/106zF.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/106zF.png" alt="Wiring"></a></p>

<p>Configure the outputs and inputs in <code>setup</code>:</p>

<pre><code>pinMode(2, INPUT_PULLUP);
pinMode(3, INPUT_PULLUP);
pinMode(4, INPUT_PULLUP);
pinMode(5, INPUT_PULLUP);
pinMode(6, INPUT_PULLUP);
pinMode(7, INPUT_PULLUP);
pinMode(8, INPUT_PULLUP);
pinMode(9, INPUT_PULLUP);
pinMode(10, INPUT);
pinMode(11, INPUT);
pinMode(12, INPUT);
pinMode(13, INPUT);
pinMode(14, INPUT); //A0
pinMode(15, INPUT); //A1
pinMode(16, INPUT); //A2
pinMode(17, INPUT); //A3
pinMode(18, INPUT); //A4
</code></pre>

<p>Make a function to scan the rows into an array of bytes:</p>

<pre><code>void scan_rows(uint8_t *rows)
{
    uint8_t i, j;

    for (i = 0; i &lt; 8; i++)
    {
        if (i)
        {
            pinMode(i+9, INPUT);
        }
        pinMode(i+10, OUTPUT);
        digitalWrite(i+10, LOW);
        for (j = 2; j &lt;= 9; j++)
        {
            rows[i] &lt;&lt;= 1;
            if (digitalRead(j))
                rows[i] |= 1;
        }
    }
    pinMode(18, INPUT);
}
</code></pre>

<p>Now, just call that function with a pointer to an array with 8 bytes in it whenever you need to scan the board. Each byte in the array represents one of the rows and each bit represents a column.</p>

<p><sub>[moderator note: This answer appears in this thread as a result of a merge]</sub></p>
