When my years back I used a 74LS448 and a 74LS447 to drive a bcd screen here is a simple
hex to seven segment converter four inputs and 7 outputs   I did not include the  select
mux for switching  displays

 The circuit to mux the displays I do not deal with it in this module

The RTL view

library ieee;
use ieee.std_logic_arith.all;
use ieee.std_logic_unsigned.all;
use ieee.std_logic_1164.all;
entity seven_segment  is
port(
 
 hex_in :in std_logic_vector ( 3  downto 0);
 seven_seg_out        : out  std_logic_vector  (6 downto 0)
 
 );
end;

 architecture seven_seg_arc of seven_segment is
       

begin
 
process (hex_in)
 
  begin
     
 case (  hex_in ) is                                 --abcdefg
   when  "0000" =>  seven_seg_out  <= "0000001";      -- 0
   when  "0001" =>  seven_seg_out  <= "1001111";      -- 1
   when  "0010" =>  seven_seg_out  <= "0010010";      -- 2
   when  "0011" =>  seven_seg_out  <= "0000110";   -- 3
   when  "0100" =>  seven_seg_out  <= "1001100";   -- 4
   when  "0101" =>  seven_seg_out  <= "0100100";   -- 5
   when  "0110" =>  seven_seg_out  <= "0100000";      -- 6
   when  "0111" =>  seven_seg_out  <= "0001111";   -- 7
   when  "1000" =>  seven_seg_out  <= "0000000";   -- 8
   when  "1001" =>  seven_seg_out  <= "0000100";   -- 9
   when  "1010" =>  seven_seg_out  <= "0001000";   -- A
   when  "1011" =>  seven_seg_out  <= "1100000";   -- B
   when  "1100" =>  seven_seg_out  <= "0110001";   -- C
   when  "1101" =>  seven_seg_out  <= "1000010";   -- D
   when  "1110" =>  seven_seg_out  <= "0110000";   -- E
   when  "1111" =>  seven_seg_out  <= "0111000";   -- F
   when  others =>   seven_seg_out <= "0000000"; 

   end case;

end process;

end; -- seven_seg_arc