利用JAVA语言设计一个简单的科学计算器，实现加减乘除及开根号、对数、平方、三角正/余弦、求倒数、进制转换的简单功能。设计要求：由于现代用户更倾向于由鼠标方便操作的图形用户界面，所以采用GUI来实现计算器，并采用Swing组件，AWT事件处理等实现具体功能。

这是一个简单的JAVA语言设计科学计算器的示例代码，实现了加减乘除、开根号、对数、平方、三角正/余弦、求倒数、进制转换等功能，采用了Swing组件和AWT事件处理实现。

import javax.swing.*;
import java.awt.*;
import java.awt.event.*;

public class ScientificCalculator extends JFrame implements ActionListener {

    private JTextField inputText;
    private JButton addButton, subtractButton, multiplyButton, divideButton, sqrtButton, logButton, squareButton, sinButton, cosButton, reciprocalButton, convertButton;
    private String operator = "";
    private double number = 0;
    private boolean start = true;

    public ScientificCalculator() {
        setTitle("科学计算器");
        setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        setSize(300, 300);
        setLayout(new BorderLayout());

        inputText = new JTextField();
        inputText.setHorizontalAlignment(JTextField.RIGHT);

        addButton = new JButton("+");
        subtractButton = new JButton("-");
        multiplyButton = new JButton("*");
        divideButton = new JButton("/");
        sqrtButton = new JButton("√");
        logButton = new JButton("log");
        squareButton = new JButton("x^2");
        sinButton = new JButton("sin");
        cosButton = new JButton("cos");
        reciprocalButton = new JButton("1/x");
        convertButton = new JButton("转换");

        JPanel buttonPanel = new JPanel();
        buttonPanel.setLayout(new GridLayout(4, 3));
        buttonPanel.add(addButton);
        buttonPanel.add(subtractButton);
        buttonPanel.add(multiplyButton);
        buttonPanel.add(divideButton);
        buttonPanel.add(sqrtButton);
        buttonPanel.add(logButton);
        buttonPanel.add(squareButton);
        buttonPanel.add(sinButton);
        buttonPanel.add(cosButton);
        buttonPanel.add(reciprocalButton);
        buttonPanel.add(convertButton);

        addButton.addActionListener(this);
        subtractButton.addActionListener(this);
        multiplyButton.addActionListener(this);
        divideButton.addActionListener(this);
        sqrtButton.addActionListener(this);
        logButton.addActionListener(this);
        squareButton.addActionListener(this);
        sinButton.addActionListener(this);
        cosButton.addActionListener(this);
        reciprocalButton.addActionListener(this);
        convertButton.addActionListener(this);

        add(inputText, BorderLayout.NORTH);
        add(buttonPanel, BorderLayout.CENTER);
        setVisible(true);
    }

    public void actionPerformed(ActionEvent e) {
        if (e.getSource() == addButton) {
            calculate();
            operator = "+";
            start = true;
        } else if (e.getSource() == subtractButton) {
            calculate();
            operator = "-";
            start = true;
        } else if (e.getSource() == multiplyButton) {
            calculate();
            operator = "*";
            start = true;
        } else if (e.getSource() == divideButton) {
            calculate();
            operator = "/";
            start = true;
        } else if (e.getSource() == sqrtButton) {
            number = Double.parseDouble(inputText.getText());
            inputText.setText(String.valueOf(Math.sqrt(number)));
        } else if (e.getSource() == logButton) {
            number = Double.parseDouble(inputText.getText());
            inputText.setText(String.valueOf(Math.log10(number)));
        } else if (e.getSource() == squareButton) {
            number = Double.parseDouble(inputText.getText());
            inputText.setText(String.valueOf(Math.pow(number, 2)));
        } else if (e.getSource() == sinButton) {
            number = Double.parseDouble(inputText.getText());
            inputText.setText(String.valueOf(Math.sin(number)));
        } else if (e.getSource() == cosButton) {
            number = Double.parseDouble(inputText.getText());
            inputText.setText(String.valueOf(Math.cos(number)));
        } else if (e.getSource() == reciprocalButton) {
            number = Double.parseDouble(inputText.getText());
            inputText.setText(String.valueOf(1 / number));
        } else if (e.getSource() == convertButton) {
            String input = inputText.getText();
            if (input.startsWith("0x")) {
                int number = Integer.parseInt(input.substring(2), 16);
                inputText.setText(String.valueOf(number));
            } else if (input.startsWith("0b")) {
                int number = Integer.parseInt(input.substring(2), 2);
                inputText.setText(String.valueOf(number));
            } else {
                int number = Integer.parseInt(input);
                inputText.setText(Integer.toHexString(number));
            }
        }
    }

    private void calculate() {
        if (start) {
            number = Double.parseDouble(inputText.getText());
            start = false;
        } else {
            switch (operator) {
                case "+":
                    number += Double.parseDouble(inputText.getText());
                    break;
                case "-":
                    number -= Double.parseDouble(inputText.getText());
                    break;
                case "*":
                    number *= Double.parseDouble(inputText.getText());
                    break;
                case "/":
                    number /= Double.parseDouble(inputText.getText());
                    break;
            }
        }
        inputText.setText(String.valueOf(number));
    }

    public static void main(String[] args) {
        new ScientificCalculator();
    }

}

该计算器实现了基本的加减乘除功能，以及开根号、对数、平方、三角正/余弦、求倒数、进制转换等科学计算功能。用户可以通过点击GUI界面上的按钮实现相应的功能。