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Logic Design Fundamentals - 2

Logic Design Fundamentals - 2. Lecture L1.2. Logic Design Fundamentals - 2. Basic Gates Basic Combinational Circuits Basic Sequential Circuits. Basic Combinational Circuits. Multiplexers 7-Segment Decoder Comparators Decoders Adders Shifters Code Converters

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Logic Design Fundamentals - 2

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  1. Logic Design Fundamentals - 2 Lecture L1.2

  2. Logic Design Fundamentals - 2 • Basic Gates • Basic Combinational Circuits • Basic Sequential Circuits

  3. Basic Combinational Circuits • Multiplexers • 7-Segment Decoder • Comparators • Decoders • Adders • Shifters • Code Converters • Arithmetic Logic Units • ROM

  4. Combinational Logic inputs outputs Combinational Logic Outputs depend only on the current inputs

  5. Multiplexers A multiplexer is a digital switch MUX 1 output, Z = X(s) 2n inputs X(0, 2n -1) n control lines s( 0, n-1)

  6. 4 x 1 MUX s1 s0 Y 0 0 C0 0 1 C1 1 0 C2 1 1 C3 Multiplexers C0 C1 Y C2 C3 s1 s0

  7. 4 x 1 MUX Multiplexers s1 s0 Y C0 0 0 C0 0 1 C1 1 0 C2 1 1 C3 C1 Y C2 C3 s1 s0 A multiplexer is a digital switch 0 0

  8. 4 x 1 MUX Multiplexers s1 s0 Y C0 0 0 C0 0 1 C1 1 0 C2 1 1 C3 C1 Y C2 C3 s1 s0 0 1

  9. 4 x 1 MUX Multiplexers s1 s0 Y C0 0 0 C0 0 1 C1 1 0 C2 1 1 C3 C1 Y C2 C3 s1 s0 1 0

  10. 4 x 1 MUX Multiplexers s1 s0 Y C0 0 0 C0 0 1 C1 1 0 C2 1 1 C3 C1 Y C2 C3 s1 s0 1 1

  11. A 2 x 1 MUX Behavior if (s0 = '0') then Z := A; else Z := B; end if;

  12. if (s0 = '0') then A := C0; B := C2; else A := C1; B := C3; end if; A 4 x 1 MUX if (s1 = '0') then if (s0 = '0') then Z := C0; else Z := C1; end if; else if (s0 = '0') then Z := C2; else Z := C3; end if; end if; if (s1 = '0') then Z := A; else Z := B; end if;

  13. A 4 x 1 MUX case s is when "00" => Z <= C0; when "01" => Z <= C1; when "10" => Z <= C2; when others => Z <= C3; end case;

  14. n-line 2-to-1 Multiplexer n-line 2 x 1 MUX a(n-1:0) y(n-1:0) b(n-1:0) sel y 0 a 1 b sel

  15. a(n-1:0) n-line 2 x 1 y(n-1:0) MUX b(n-1:0) sel An n-line 2 x 1 MUX 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;

  16. generic statement defines width of bus Entity Each entity must begin with these library and use statements 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; port statement defines inputs and outputs

  17. Entity Mode: in or out 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; Data type: STD_LOGIC, STD_LOGIC_VECTOR(width-1 downto 0);

  18. Standard Logic library IEEE; use IEEE.std_logic_1164.all; 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

  19. 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;

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

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

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

  23. An 8-line 4 x 1 multiplexer library IEEE; use IEEE.std_logic_1164.all; entity mux4g is generic(width:positive := 8); 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. Sel y “00” a “01” b “10” c “11” d 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; Note implies operator => Must include ALL possibilities in case statement

  25. 7-Segment Display seg7dec D(3:0) AtoG(6:0) Truth table D a b c d e f g 8 1 1 1 1 1 1 1 9 1 1 1 1 0 1 1 A 1 1 1 0 1 1 1 b 0 0 1 1 1 1 1 C 1 0 0 1 1 1 0 d 0 1 1 1 1 0 1 E 1 0 0 1 1 1 1 F 1 0 0 0 1 1 1 D a b c d e f g 0 1 1 1 1 1 1 0 1 0 1 1 0 0 0 0 2 1 1 0 1 1 0 1 3 1 1 1 1 0 0 1 4 0 1 1 0 0 1 1 5 1 0 1 1 0 1 1 6 1 0 1 1 1 1 1 7 1 1 1 0 0 0 0

  26. 7-Segment Display Verilog case(D) 0: AtoG = 7'b1111110; 1: AtoG = 7'b0110000; 2: AtoG = 7'b1101101; 3: AtoG = 7'b1111001; 4: AtoG = 7'b0110011; 5: AtoG = 7'b1011011; 6: AtoG = 7'b1011111; 7: AtoG = 7'b1110000; 8: AtoG = 7'b1111111; 9: AtoG = 7'b1111011; 'hA: AtoG = 7'b1110111; 'hb: AtoG = 7'b0011111; 'hC: AtoG = 7'b1001110; 'hd: AtoG = 7'b0111101; 'hE: AtoG = 7'b1001111; 'hF: AtoG = 7'b1000111; default: AtoG = 7'b1111110; // 0 endcase Behavior seg7dec D(3:0) AtoG(6:0)

  27. 7-Segment Display VHDL -- seg7dec with digit select ssg <= "1001111" when "0001", --1 "0010010" when "0010", --2 "0000110" when "0011", --3 "1001100" when "0100", --4 "0100100" when "0101", --5 "0100000" when "0110", --6 "0001111" when "0111", --7 "0000000" when "1000", --8 "0000100" when "1001", --9 "0001000" when "1010", --A "1100000" when "1011", --b "0110001" when "1100", --C "1000010" when "1101", --d "0110000" when "1110", --E "0111000" when "1111", --F "0000001" when others; --0 Behavior (Active LOW) AtoG seg7dec digit(3:0) sseg(6:0)

  28. Comparators Recall that an XNOR gate can be used as an equality detector XNOR X if X = Y then Z <= '1'; else Z <= '0'; end if; Z Y Z = !(X $ Y) Z = X xnor Y Z = ~(X @ Y) X Y Z 0 0 1 0 1 0 1 0 0 1 1 1

  29. 4-Bit Equality Comparator A: in STD_LOGIC_VECTOR(3 downto 0); B: in STD_LOGIC_VECTOR(3 downto 0); A_EQ_B: out STD_LOGIC;

  30. library IEEE; use IEEE.STD_LOGIC_1164.ALL; use IEEE.STD_LOGIC_ARITH.ALL; use IEEE.STD_LOGIC_UNSIGNED.ALL; entity eqdet4 is Port ( A : in std_logic_vector(3 downto 0); B : in std_logic_vector(3 downto 0); A_EQ_B : out std_logic); end eqdet4; architecture Behavioral of eqdet4 is signal C: std_logic_vector(3 downto 0); begin C <= A xnor B; A_EQ_B <= C0 and C1 and C2 and C3; end Behavioral;

  31. comp A_EQ_B A(n-1:0) A_GT_B A_LT_B B(n-1:0) A_UGT_B A_ULT_B Comparators A, B signed A, B unsigned Signed: 2's complement signed numbers

  32. -- Comparator for unsigned and signed numbers library IEEE; use IEEE.std_logic_1164.all; use IEEE.std_logic_arith.all; use IEEE.std_logic_unsigned.all; entity comp is generic(width:positive); port ( A: in STD_LOGIC_VECTOR(width-1 downto 0); B: in STD_LOGIC_VECTOR(width-1 downto 0); A_EQ_B: out STD_LOGIC; A_GT_B: out STD_LOGIC; A_LT_B: out STD_LOGIC; A_ULT_B: out STD_LOGIC; A_UGT_B: out STD_LOGIC ); end comp; comp A_EQ_B A(n-1:0) A_GT_B A_LT_B B(n-1:0) A_UGT_B A_ULT_B

  33. architecture comp_arch of comp is begin CMP: process(A,B) variable AVS, BVS: signed(width-1 downto 0); begin for i in 0 to width-1 loop AVS(i) := A(i); BVS(i) := B(i); end loop; A_EQ_B <= '0'; A_GT_B <= '0'; A_LT_B <= '0'; A_ULT_B <= '0'; A_UGT_B <= '0'; if (A = B) then A_EQ_B <= '1'; end if; if (AVS > BVS) then A_GT_B <= '1'; end if; if (AVS < BVS) then A_LT_B <= '1'; end if; if (A > B) then A_UGT_B <= '1'; end if; if (A < B) then A_ULT_B <= '1'; end if; end process CMP; end comp_arch; comp A_EQ_B A(n-1:0) A_GT_B A_LT_B B(n-1:0) A_UGT_B A_ULT_B Note: All outputs must be assigned some value. The last signal assignment in a process is the value assigned

  34. 4-Bit Comparator

  35. Full Adder Truth table Ci Si Ai Ci+1 Bi Behavior Ci+1:Si = Ci + Ai + Bi

  36. Full Adder Block Diagram

  37. 4-Bit Adder C 1 1 1 0 0:A 0 1 1 0 1 0:B 0 0 1 1 1 C4:S 1 0 1 0 0

  38. library IEEE; use IEEE.STD_LOGIC_1164.all; use IEEE.STD_LOGIC_unsigned.all; entity adder4 is port( A : in STD_LOGIC_VECTOR(3 downto 0); B : in STD_LOGIC_VECTOR(3 downto 0); carry : out STD_LOGIC; S : out STD_LOGIC_VECTOR(3 downto 0) ); end adder4; architecture adder4 of adder4 is begin process(A,B) variable temp: STD_LOGIC_VECTOR(4 downto 0); begin temp := ('0' & A) + ('0' & B); S <= temp(3 downto 0); carry <= temp(4); end process; end adder4;

  39. 4-Bit Adder

  40. 3-to-8 Decoder A: in STD_LOGIC_VECTOR(2 downto 0); Y: out STD_LOGIC_VECTOR(0 to 7); Behavior for i in 0 to 7 loop if(i = conv_integer(A)) then Y(i) <= ‘1’; else Y(i) <= ‘0’; end if; end loop;

  41. library IEEE; use IEEE.STD_LOGIC_1164.all; use IEEE.STD_LOGIC_arith.all; use IEEE.STD_LOGIC_unsigned.all; entity decode38 is port( A : in STD_LOGIC_VECTOR(2 downto 0); Y : out STD_LOGIC_VECTOR(0 to 7) ); end decode38; architecture decode38 of decode38 is begin process(A) variable j: integer; begin j := conv_integer(A); for i in 0 to 7 loop if(i = j) then Y(i) <= '1'; else Y(i) <= '0'; end if; end loop; end process; end decode38; 3-to-8 Decoder

  42. 3-to-8 Decoder

  43. Shifters Shift right Shift left Arithmetic shift right

  44. shift4.vhd library IEEE; use IEEE.std_logic_1164.all; use IEEE.std_logic_unsigned.all; entity shifter is generic(width:positive := 4); port ( D: in STD_LOGIC_VECTOR(width-1 downto 0); s: in STD_LOGIC_VECTOR(1 downto 0); Y: out STD_LOGIC_VECTOR(width-1 downto 0) ); end shifter;

  45. architecture shifter_arch of shifter is begin shift_1: process(D, s) begin case s is when "00" => -- no shift Y <= D; when "01" => -- U2/ Y <= '0' & D(width-1 downto 1); when "10" => -- 2* Y <= D(width-2 downto 0) & '0'; when "11" => -- 2/ Y <= D(width-1) & D(width-1 downto 1); whenothers => -- no shift Y <= D; end case; end process shift_1; end shifter_arch;

  46. Code Converters • Gray Code Converter • Binary-to-BCD Converter

  47. Gray Code Definition: An ordering of 2n binary numbers such that only one bit changes from one entry to the next. Binary coding {0...7}: {000, 001, 010, 011, 100, 101, 110, 111} Gray coding {0...7}: {000, 001, 011, 010, 110, 111, 101, 100} Not unique One method for generating a Gray code sequence: Start with all bits zero and successively flip the right-most bit that produces a new string.

  48. Binary - Gray Code Conversions Gray code: G(i), i = n – 1 downto 0 Binary code: B(i), i = n – 1 downto 0 Binary coding {0...7}: {000, 001, 010, 011, 100, 101, 110, 111} Gray coding {0...7}: {000, 001, 011, 010, 110, 111, 101, 100} Convert Binary to Gray: Copy the most significant bit. For each smaller i G(i) = B(i+1) xor B(i) Convert Gray to Binary: Copy the most significant bit. For each smaller i B(i) = B(i+1) xor G(i)

  49. bin2gray.vhd library IEEE; use IEEE.STD_LOGIC_1164.all; entity bin2gray is generic(width:positive := 3); port( B : in STD_LOGIC_VECTOR(width-1 downto 0); G : out STD_LOGIC_VECTOR(width-1 downto 0) ); end bin2gray; architecture bin2gray of bin2gray is begin process(B) begin G(width-1) <= B(width-1); for i in width-2 downto 0 loop G(i) <= B(i+1) xor B(i); end loop; end process; end bin2gray;

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