1. Multiplexers Section 3-7 Mano & Kime

2. Multiplexers & Demultiplexers Multiplexers (Selectors) Lab 1 – Behavioral VHDL -- Multiplexers MUX as a Universal Element

3. 4– to– 1- Line Multiplexer

4. 4–to–1-Line Multiplexer with Transmission Gates

5. Quadruple 2–to–1-Line Multiplexer

7. Typical uses

8. Multiplexers Multiplexers (Selectors) Lab 1 – Behavioral VHDL -- Multiplexers MUX as a Universal Element

9. Combinational Circuit Example n-line 2-to-1 Multiplexer n-line 2 x 1 MUX a(n-1:0) b(n-1:0) y(n-1:0) sel sel y 0 a 1 b

10. library IEEE; use IEEE.std_logic_1164.all; entity mux2g is generic (width:positive); port ( a: in STD_LOGIC_VECTOR(width-1 downto 0); b: in STD_LOGIC_VECTOR(width-1 downto 0); sel: in STD_LOGIC; y: out STD_LOGIC_VECTOR(width-1 downto 0) ); end mux2g; An n-line 2 x 1 MUX a(n-1:0) b(n-1:0) y(n-1:0) sel n-line 2 x 1 MUX

11. library IEEE; use IEEE.std_logic_1164.all; entity mux2g is generic (width:positive); port ( a: in STD_LOGIC_VECTOR(width-1 downto 0); b: in STD_LOGIC_VECTOR(width-1 downto 0); sel: in STD_LOGIC; y: out STD_LOGIC_VECTOR(width-1 downto 0) ); end mux2g; Entity Each entity must begin with these library and use statements port statement defines inputs and outputs generic statement defines width of bus

12. library IEEE; use IEEE.std_logic_1164.all; entity mux2g is generic (width:positive); port ( a: in STD_LOGIC_VECTOR(width-1 downto 0); b: in STD_LOGIC_VECTOR(width-1 downto 0); sel: in STD_LOGIC; y: out STD_LOGIC_VECTOR(width-1 downto 0) ); end mux2g; Entity Mode: in or out Data type: STD_LOGIC, STD_LOGIC_VECTOR(width-1 downto 0);

13. Standard Logic type std_ulogic is (‘U’, -- Uninitialized ‘X’ -- Forcing unknown ‘0’ -- Forcing zero ‘1’ -- Forcing one ‘Z’ -- High impedance ‘W’ -- Weak unknown ‘L’ -- Weak zero ‘H’ -- Weak one ‘-’); -- Don’t care library IEEE; use IEEE.std_logic_1164.all;

14. Standard Logic Type std_ulogic is unresolved. Resolved signals provide a mechanism for handling the problem of multiple output signals connected to one signal. subtype std_logic is resolved std_ulogic;

15. architecture mux2g_arch of mux2g is begin mux2_1: process(a, b, sel) begin if sel = '0' then y <= a; else y <= b; end if; end process mux2_1; end mux2g_arch; Architecture a(n-1:0) b(n-1:0) y(n-1:0) sel n-line 2 x 1 MUX Note: <= is signal assignment

16. architecture mux2g_arch of mux2g is begin mux2_1: process(a, b, sel) begin if sel = '0' then y <= a; else y <= b; end if; end process mux2_1; end mux2g_arch; Architecture entity name process sensitivity list Sequential statements (if…then…else) must be in a process Note begin…end in process Note begin…end in architecture

17. Digilab2 – DIO1 Boards Spartan II FPGA 8 LEDs LD 8 Switches SW 4 Pushbuttons BTN Four 7-segment displays Pushbutton bn 74HC373 latch ldg <= ‘1’

18. Top-level Design – Lab 1

19. library IEEE; use IEEE.std_logic_1164.all; entity lab1 is port ( SW: in STD_LOGIC_VECTOR (1 to 8); BTN4: in STD_LOGIC; ldg: out STD_LOGIC; LD: out STD_LOGIC_VECTOR (1 to 4) ); end lab1;

20. architecture lab1_arch of lab1 is component mux2g generic(width:positive); port ( a: in STD_LOGIC_VECTOR (width-1 downto 0); b: in STD_LOGIC_VECTOR (width-1 downto 0); sel: in STD_LOGIC; y: out STD_LOGIC_VECTOR (width-1 downto 0) ); end component; constant bus_width: positive := 4; begin ldg <= '1'; -- enable 74HC373 latch SWmux: mux2g generic map(width => bus_width) port map (a => SW(1 to 4), b => SW(5 to 8), sel => BTN4, y => LD); end lab1_arch;

22. An n-line 4 x 1 multiplexer a(n-1:0) b(n-1 :0) y(n-1 :0) sel(1:0) 8-line 4 x 1 MUX c(n-1 :0) d(n-1 :0) Sely “00”a “01”b “10”c “11”d

23. An 8-line 4 x 1 multiplexer library IEEE; use IEEE.std_logic_1164.all; entity mux4g is generic(width:positive); port ( a: in STD_LOGIC_VECTOR (width-1 downto 0); b: in STD_LOGIC_VECTOR (width-1 downto 0); c: in STD_LOGIC_VECTOR (width-1 downto 0); d: in STD_LOGIC_VECTOR (width-1 downto 0); sel: in STD_LOGIC_VECTOR (1 downto 0); y: out STD_LOGIC_VECTOR (width-1 downto 0) ); end mux4g;

24. Example of case statement architecture mux4g_arch of mux4g is begin process (sel, a, b, c, d) begin case sel is when "00" => y <= a; when "01" => y <= b; when "10" => y <= c; when others => y <= d; end case; end process; end mux4g_arch; Must include ALL posibilities in case statement Note implies operator => Sely “00”a “01”b “10”c “11”d

25. VHDL Architecture Structure architecture name_arch of name is begin end name_arch; Signal assignments Concurrent statements Process 1 Process 2 Concurrent statements Processes contain sequential statements, but execute concurrently within the architecture body

26. VHDL Process P1: process (<sensitivity list) begin end process P1; Optional process label Within a process: Variables are assigned using := and are updated immediately. Signals are assigned using <= and are updated at the end of the process.

27. Multiplexers Multiplexers (Selectors) Lab 1 – Behavioral VHDL -- Multiplexers MUX as a Universal Element

28. Multiplexer as universal combinational module connect input variables x to select inputs of multiplexer s set data inputs to multiplexer equal to values of function for corresponding assignment of select variables using a variable at data inputs reduces size of the multiplexer

29. Implementing a Boolean Function with a Multiplexer

30. Implementing a Four- Input Function with a Multiplexer

31. Networks with 2-input multiplexers

32. Implementation of SFs with network of MUXes

33. Design of networks with MUXes

34. Example

35. Ordering of variables in subtrees affects the number of MUXes

36. Example of Shannon’s Decomposition F = x 3 (x 1 + x 2 x 0 ) Implemented using a multiplexer network

37. F = x 3 (x 1 + x 2 x 0 ) Start with any variable - x 0 for example x 0 = 0 x 0 = 1 F = x 3 x 1 F = x 3 (x 1 + x 2 )

38. F = x 3 (x 1 + x 2 x 0 ) Then x ! for example x 0 = 0 x 0 = 1 F = x 3 x 1 F = x 3 (x 1 + x 2 ) x 1 = 0 x 1 = 1 F = 0 F = x 3 x 1 = 0 x 1 = 1 F = x 3 x 2 F = x 3

39. F = x 3 (x 1 + x 2 x 0 ) Then x 2 for example x 0 = 0 x 0 = 1 F = x 3 x 1 F = x 3 (x 1 + x 2 ) x 1 = 0 x 1 = 1 F = 0 F = x 3 x 1 = 0 x 1 = 1 F = x 3 x 2 F = x 3 x 2 = 0 x 2 = 1 F = 0 F = x 3

40. F = x 3 (x 1 + x 2 x 0 ) x 0 = 0 x 0 = 1 F = x 3 x 1 F = x 3 (x 1 + x 2 ) x 1 = 0 x 1 = 1 F = 0 F = x 3 x 1 = 0 x 1 = 1 F = x 3 x 2 F = x 3 x 2 = 0 x 2 = 1 F = 0 F = x 3 Inputs

41. F = x 3 (x 1 + x 2 x 0 ) x 0 = 0 x 0 = 1 F = x 3 x 1 F = x 3 (x 1 + x 2 ) x 1 = 0 x 1 = 1 F = 0 F = x 3 x 1 = 0 x 1 = 1 F = x 3 x 2 F = x 3 x 2 = 0 x 2 = 1 F = 0 F = x 3 MUX Select Lines

42. x 1 = 0 x 0 = 0 x 0 = 1 F = x 3 x 1 F = x 3 (x 1 + x 2 ) x 1 = 1 F = 0 F = x 3 x 1 = 0 x 1 = 1 F = x 3 x 2 F = x 3 x 2 = 0 x 2 = 1 F = 0 F = x 3 1 0 sel x3x1x3x1 x 3 (x 1 + x 2 ) x0x0 F

43. x 1 = 0 x 0 = 0 x 0 = 1 F = x 3 x 1 F = x 3 (x 1 + x 2 ) x 1 = 1 F = 0 F = x 3 x 1 = 0 x 1 = 1 F = x 3 x 2 F = x 3 x 2 = 0 x 2 = 1 F = 0 F = x 3 x3x1x3x1 1 0 sel x 3 (x 1 + x 2 ) 1 0 sel x0x0 x1x1 0 x3x3 The branch for x 0 = 0 F

44. x 1 = 0 x 0 = 0 x 0 = 1 F = x 3 x 1 F = x 3 (x 1 + x 2 ) x 1 = 1 F = 0 F = x 3 x 1 = 0 x 1 = 1 F = x 3 x 2 F = x 3 x 2 = 0 x 2 = 1 F = 0 F = x 3 x3x1x3x1 1 0 sel x 3 (x 1 + x 2 ) 1 0 sel x0x0 x1x1 0 x3x3 1 0 x1x1 x3x2x3x2 x3x3 The branch for x 0 = 1 F

45. x 1 = 0 x 0 = 0 x 0 = 1 F = x 3 x 1 F = x 3 (x 1 + x 2 ) x 1 = 1 F = 0 F = x 3 x 1 = 0 x 1 = 1 F = x 3 x 2 F = x 3 x 2 = 0 x 2 = 1 F = 0 F = x 3 x3x1x3x1 1 0 sel x 3 (x 1 + x 2 ) 1 0 sel x0x0 x1x1 0 x3x3 1 0 x1x1 x3x2x3x2 x3x3 The branch for x 1 = 0 1 0 sel x2x2 x3x3 0 F

46. F = x 3 (x 1 + x 2 x 0 ) Starting with x 0 Shannon’s Decomposition 4 Multiplexers 1 0 sel 1 0 x0x0 x1x1 0 x3x3 1 0 x1x1 x3x3 1 0 x2x2 x3x3 0 F

47. F = x 3 (x 1 + x 2 x 0 ) Starting with x 1 Shannon’s Decomposition 3 Multiplexers 1 0 sel 1 0 x1x1 x0x0 0 1 0 x2x2 x3x3 F x3x3 0

48. 16-input tree multiplexer