How to manipulate and use a layout and arrange objects the way I want?

A layout you may wish to consider is the BoxLayout (I personally always tend to lean toward BoxLayout because it is both easy and versatile when used in combinations): create a JPanel that has a page axis box layout, then add the components to this layout.

Here's a quick revision, you can of course alter the prettiness of the layout bay adding borders and/or chaning the layouts of the other panels.

Java code:

import javax.swing.JButton;
import javax.swing.JFrame;
import javax.swing.JPanel;
import javax.swing.JTextField;
import javax.swing.JLabel;
import javax.swing.BoxLayout;
import java.awt.Color;
import java.awt.Container;
import java.awt.BorderLayout;
import java.awt.FlowLayout;
import java.awt.GridLayout;
import java.awt.event.ActionEvent;
import java.awt.event.ActionListener;

public class Test extends JFrame implements ActionListener
{
    public static final int WIDTH = 400;
    public static final int HEIGHT = 300;
 

    private JTextField binaryText;
    private JTextField decimalText;

    private String decimal = "No Binary to Convert";
    private String binary = "No Decimal to Convert";

    public Test( )
    {
  setSize(WIDTH, HEIGHT);

  JPanel main = new JPanel(  );
  main.setLayout( new BoxLayout(main, BoxLayout.PAGE_AXIS ));
        //addWindowListener(new WindowDestroyer( ));
        setTitle("Binary/Decimal Number Converter");
        Container contentPane = getContentPane( );
 

       // contentPane.setLayout(new BorderLayout( ));

        JPanel buttonPanel = new JPanel( );

        buttonPanel.setLayout(new FlowLayout( ));

        JButton toDecButton = new JButton("To Base 10");
        toDecButton.addActionListener(this);
        buttonPanel.add(toDecButton);

        JButton toBinButton = new JButton("To Base 2");
        toBinButton.addActionListener(this);
        buttonPanel.add(toBinButton);

        JButton clearButton = new JButton("Clear");
        clearButton.addActionListener(this);
        buttonPanel.add(clearButton);

        JButton exitButton = new JButton("Exit");
        exitButton.addActionListener(this);
        buttonPanel.add(exitButton);

       // contentPane.add(buttonPanel, BorderLayout.SOUTH);

        JPanel textPanel = new JPanel( );

  //contentPane.setLayout(new GridLayout(6, 1));

  JLabel binLabel = new JLabel("Binary number:");
        //contentPane.add(binLabel);

        binaryText = new JTextField(20);
        binaryText.setBackground(Color.WHITE);
  textPanel.add(binLabel);
        textPanel.add(binaryText);
        //contentPane.add(textPanel);

  JLabel decLabel = new JLabel("Decimal number:");
        //contentPane.add(decLabel);

  decimalText = new JTextField(20);
  decimalText.setBackground(Color.WHITE);
  //textPanel.add(decimalText);

  main.add( textPanel );
  main.add( decLabel );
  main.add( decimalText );
  main.add( buttonPanel );
  getContentPane().add(main);
  pack();
        //contentPane.add(textPanel);

    }

    public void actionPerformed(ActionEvent e)
    {
        String actionCommand = e.getActionCommand( );
        if (actionCommand.equals("To Base 10"))
            decimal = binaryText.getText( );
        else if (actionCommand.equals("To Base 2"))
            binary = decimalText.getText( );
        else if (actionCommand.equals("Clear")) {
            binaryText.setText("");
            decimalText.setText("");
  }
        else if (actionCommand.equals("Exit"))
            System.exit(0);
        else
            binaryText.setText("Error in conversion");
     }

    public static void main(String[] args)
    {
        Test guiMemo = new Test( );
        guiMemo.setVisible(true);
    }
}

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