1. Multiplexer as a Universal Element Discussion D2.6 Example 9

2. MUX as a Universal Element

3. Example f = x*~y + x*z + ~y*z

4. Step 1 f = x*~y + x*z + ~y*z If x = 0 f = v = ~y*z If x = 1 f = w = ~y + z + ~y*z

5. Step 2 If x = 0 f = v = ~y*z If x = 1 f = w = ~y + z + ~y*z If y = 0 v = z If y = 1 v = 0 If y = 0 w = 1 If y = 1 w = z f = x*~y + x*z + ~y*z

7. -- Example 9: Using 2-to-1 MUXs -- as a universal function generator library IEEE; use IEEE.STD_LOGIC_1164.all; entity muxu is port( x : in STD_LOGIC; y : in STD_LOGIC; z : in STD_LOGIC; f : out STD_LOGIC ); end muxu; architecture muxu of muxu is component mux21b port( a : in std_logic; b : in std_logic; s : in std_logic; y : out std_logic); end component; signal v, w: STD_LOGIC;

8. begin M1 : mux21b port map( a => z, b => '0', s => y, y => v ); M2 : mux21b port map( a => '1', b => z, s => y, y => w ); M3 : mux21b port map( a => v, b => w, s => x, y => f ); end muxu;

9. Aldec Active-HDL Simulation