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Thus, while it s easy to multiply or divide by any integral power of ten in the decimal system, it s equally easy to multiply or divide by any integral power of two in the binary system. For instance, consider a binary number, N 101101; suppose, for example, that we wish to multiply or divide N by say eight, which is 1000 in the binary system. Either operation is very simply done, as follows, 101101 1000 101101000 and 101101 101:101 1000

try { // Create a new message with values from dialog box. Message newMessage = new MimeMessage(session); newMessage.setFrom(new InternetAddress(dialog.getFrom())); newMessage.setRecipient(Message.RecipientType.TO, new InternetAddress(dialog.getTo())); newMessage.setSubject(dialog.getSubject()); newMessage.setSentDate(new Date()); newMessage.setText(dialog.getContent()); // Send new message. Transport.send(newMessage); } catch (Exception e) { showError("Unable to send message.", false); } }

For the same values, the corresponding operations in the decimal system would be 45 times 8 and 45 divided by 8 which, of course, cannot be done by simply moving the decimal point to the right or the left. As you can see from the above, expressing a given value in binary notation requires the writing of many more digits than in decimal notation. Thus, while the binary system is

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admirably suited for internal use in a digital computer, it is not well suited for direct use by human beings because it requires the writing down of so many digits to express even small values. This bears out the statement made previously in regard to R 2 being the ideal choice for internal computer operation, and R 10 being a good compromise for use by human beings. Now let s consider the procedures for converting a decimal number into binary form and vice versa. In stating the rules we ll make use of the terms most signi cant digit (MSD) and least signi cant digit (LSD). The MSD is simply the digit having the most value in a number, while the LSD is the digit having the least value in a number. Thus, in the decimal number 28736, 2 is the MSD, 8 is the next-most signi cant digit, and so on, until we reach 6, which is the LSD. Or, in the binary number 110101, for example, the 1 at the left-hand end is the MSD, while, going from left to right, we nally arrive at the 1 at the right-hand end, which is the LSD. With this terminology in mind, the rules for conversion from decimal to binary, and from binary to decimal, can be summarized as follows.

First, sendMessage( ) creates a MessageDialog forwarding it the message type and message passed in as arguments. The MessageDialog then collects the message properties such as the To address, the From address, and the Subject. After the message properties have been collected, a new Message object is created and populated with the properties. The new message s From address is set with the Message object s setFrom( ) method. Similarly, the Message object s setRecipient( ) method sets the new message s To address. Take note that the setRecipient( ) method also serves to set a message s CC and BCC addresses by specifying the recipient type as Message.RecipientType.CC or Message.RecipientType .BCC, respectively. The Messsage object s setSubject( ) method does just that it sets the message s subject. The setSentDate( ) method specifies the timestamp placed on the message. The setText( ) method specifies the message s text content. Finally, the message is sent with a call to Transport.send( ). JavaMail s Transport class encapsulates the protocol-specific code for sending the message, which typically is SMTP.

First, the following steps can be taken to convert a WHOLE decimal number into binary form. 1. 2. Divide the decimal number by 2; this produces a quotient plus a remainder of either 1 or 0. The remainder, 1 or 0, is the LSD in the equivalent binary number. Divide the quotient found in step (1) by 2; this produces a second quotient plus a remainder of 1 or 0. This remainder, 1 or 0, is the second least signi cant in the binary number. Continue on in this fashion, dividing each quotient by 2, until the quotient is equal to zero plus the nal remainder of 1 or 0, which is the MSD in the binary number. Example 1

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