（记数－进制转换－java）用－2为基做进制转换
这学期有门课叫做工程数学基础，第一章节我们学习一些关于记数的知识。
这里大致有几个概念要知道，第一为基，如10进制，10就是基，记做a，其次为数字符号集合s，这个又常常被称为a的完全剩余类，在s和a上存在一些约束关系，例如（未证明），s中最大元素的值小于｜a｜，s中元素的个数要等于｜a｜，在正整数领域，而s中的元素未必是一成不变的，如同3进制，我们可以使用0，1，2，同时也可以使用0，1，－1，如此，但是如果不满足以上两个条件，可能会导致，不能够表示整个数系中所有的数，这里需要注意。
同时我们不仅能够用正整数做基，还可以用负数，虚数，无理数，以及fibonacci数列作为基，如下程序（采用java）
import javax.print.DocFlavor.STRING;import javax.swing.*;import java.awt.*;import java.awt.event.*;import java.io.IOException;import java.io.StringWriter;import java.math.*;public class transform {/** * make by Edward.xu * 9.7.2012 0:30 * small version 0.2 */static JTextField deciamlField;static JTextField binaryField; static long decimal;static long binary;static String decimalNumber;static String binaryNumber;public static void main(String[] args) {// TODO Auto-generated method stub// print function,long time no to use java// to write a kitbinaryNumber = new String();decimalNumber = new String();System.out.println("徐方鑫特制-超级小型机制转换器");// create a frame which is the main panelJFrame frame = new JFrame("徐方鑫设计-must");frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);// the main panelJPanel panel = new JPanel();frame.add(panel);// i like use the box.expecially the vertical boxBox mainBox = Box.createVerticalBox();panel.add(mainBox);// to prove my write/*JLabel verionLabel = new JLabel("Version 0.1");JLabel schoolLabel = new JLabel("Master of must 2012");JLabel nameLabel = new JLabel("Made by Edward.xu");mainBox.add(verionLabel);mainBox.add(schoolLabel);mainBox.add(nameLabel);*/// the first box which tip this is decimal numberBox deciamlBox = Box.createHorizontalBox();mainBox.add(deciamlBox);JLabel deciamlLabel = new JLabel("Deciaml：");deciamlField = new JTextField();deciamlBox.add(deciamlLabel);deciamlBox.add(deciamlField);// the second box which tip this is Binary numberBox binaryBox = Box.createHorizontalBox();mainBox.add(binaryBox);JLabel binaryLabel = new JLabel("Binary：");binaryField = new JTextField();binaryBox.add(binaryLabel);binaryBox.add(binaryField);// the button start transformBox buttonBox = Box.createHorizontalBox();mainBox.add(buttonBox);JButton decToBinButton = new JButton("10 to -2");JButton binToDecButton = new JButton("-2 to 10");buttonBox.add(decToBinButton);buttonBox.add(binToDecButton); // the main function of the calculatedecToBinButton.addActionListener(new ActionListener(){public void actionPerformed(ActionEvent e1){binaryNumber = "";try{decimalNumber = deciamlField.getText();decimal = Long.parseLong(decimalNumber);// main transformwhile(decimal != 1){if((decimal%(-2))==-1) { //rewrite %,it's very necessary //System.out.print(decimal - ((-2)*(decimal / (-2) + 1))); binaryNumber = binaryNumber + String.valueOf(decimal - ((-2)*(decimal / (-2) + 1))); decimal = decimal / (-2) + 1;}else{ //System.out.print(decimal - ((-2)*(decimal / (-2)))); binaryNumber = binaryNumber + String.valueOf(decimal - ((-2)*(decimal / (-2)))); decimal = decimal / (-2);}}//System.out.print("1");binaryNumber = binaryNumber + "1";// end main transformStringBuilder reverseBinaryNumber = new StringBuilder(binaryNumber);binaryNumber = reverseBinaryNumber.reverse().toString();binaryField.setText(binaryNumber);}catch(Exception ex1){JOptionPane.showMessageDialog(null, "你是在填数字吗？");}}});binToDecButton.addActionListener(new ActionListener(){public void actionPerformed(ActionEvent e2){try{binary = 0;decimal = 0;// x/power(10,n) * power((-2),n)binaryNumber = binaryField.getText();binary = Long.parseLong(binaryNumber);decimal = binary % 10 + decimal;for (int i = binaryNumber.length() - 1; i>0 ; i--){//System.out.println(i);decimal = decimal + ((binary / (long) (Math.pow(10, i)) )* (long)Math.pow(-2, i));binary = binary - (binary / (long) (Math.pow(10, i)))*(long) Math.pow(10, i);//System.out.println(binary);}//System.out.println(decimal);decimalNumber = String.valueOf(decimal);deciamlField.setText(decimalNumber);}catch(Exception ex1){JOptionPane.showMessageDialog(null, "你是在填数字吗？");}}});// start the frame and panel，make it visibleframe.setSize(300,140);frame.setVisible(true);}}