I see a main JPanel and 6 subordinate JPanels.
The first subordinate JPanel is the display.  It would have a FlowLayout with one JLabel for the number display.
The next JPanel is the binary number display.  It would have a GridLayout with 32 JLabel fields.
The next 2 JPanels hold the JRadioButton groups.  They would have a FlowLayout, and the radio buttons would be in ButtonGroups.
The next JPanel consists of the first 3 columns of buttons.  It would have a GridLayout with 18 JButtons.
The final subordinate JPanel consists of the last 5 columns of buttons.  It would have a GridBagLayout, because of the zero and equals buttons.
The main JPanel would have a GridBagLayout.
Put this GUI together, by hand (no GUI builder) one JPanel at a time.  I would have a separate class for each subordinate JPanel, and another class for the main JPanel.  Seven classes just for the JPanels.