1. 1 Combinational Logic Lecture #6

2. 모바일컴퓨터특강 2 강의순서 Decoder 3x8 Mux 4x1 Mux 8x1 Mux 8x1 4bits Half Adder Full Adder Ripple carry Adder 4-bit Adder

3. 모바일컴퓨터특강 3 Combinational Logic One or more digital signal inputs One or more digital signal outputs Outputs are only functions of current input values (ideal) plus logic propagation delays Combinational Logic i1i1 imim O1O1 OnOn

4. 모바일컴퓨터특강 4 Combinational Logic (cont.) Combinational logic has no memory Outputs are only function of current input combination Nothing is known about past events Repeating a sequence of inputs always gives the same output sequence Sequential logic does have memory Repeating a sequence of inputs can result in an entirely different output sequence

5. 모바일컴퓨터특강 5 Combinational Logic (cont.) Design Procedure 회로 기능 명세 서술문 논리식 (Logic Expression) 최소화된 논리식 (Minimized Logic Expression) 하드웨어 논리회로 합성 (Synthesis) 구현 (Implementation) 진리표를 이용 한 정규논리식 정의 카르노맵 등을 이용하여 논리 식 단순화

6. 모바일컴퓨터특강 6 ( 참고 ) Design Entry Flow with Quartus II

7. 모바일컴퓨터특강 7 Logic simplifications Consider an automobile buzzer Buzzer = (Key In and Door Open) or (Headlight On and Door Open) B = KD + HD = (K+H)D

8. 모바일컴퓨터특강 8 Simulation Verify if b_reduced yields the same result.

9. 모바일컴퓨터특강 9 Compilation Report Verify the reduced equation with Fitter Equation & : AND ! : NOT # : OR $ : XOR

10. 모바일컴퓨터특강 10 Floorplan Verify the reduced equation with Floorplan

11. 모바일컴퓨터특강 11 Exercise (1) Simplify X = (ABC’ + B)BC’ by starting with a BDF Verify the result with compilation report & floorplan

12. 모바일컴퓨터특강 12 Exercise (2) Simplify the equations by starting with a VHDL file X = (AB + (B’+C))’ Y = (AB)’ + (B+C)’ Verify the result with compilation report & floorplan

13. 모바일컴퓨터특강 13 Exercise (3) – Entering a Truth Table with VHDL Identify the logic with compilation report & floorplan

14. 모바일컴퓨터특강 14 3-to-8, 4-to–16, n–to–2 n M0 M1 M7 A0 A1 A2 A typical 3 – to - 8 decoder circuit Decoder

15. 모바일컴퓨터특강 15 3x8 Decoder (Signal assignment, Conditional) LIBRARY ieee;-- 3x8 decoder using Boolean equations-- USE ieee.std_logic_1164.ALL; ENTITY decoder_a IS PORT(a0,a1,a2: IN std_logic; y0,y1,y2,y3,y4,y5,y6,y7 : OUT std_logic); END decoder_a ; ARCHITECTURE arc OF decoder_a IS BEGIN y0<= (NOT a2) AND (NOT a1) AND (NOT a0); y1<= (NOT a2) AND (NOT a1) AND ( a0); y2<= (NOT a2) AND ( a1) AND (NOT a0); y3<= (NOT a2) AND ( a1) AND ( a0); y4<= ( a2) AND (NOT a1) AND (NOT a0); y5<= ( a2) AND (NOT a1) AND ( a0); y6<= ( a2) AND ( a1) AND (NOT a0); y7<= ( a2) AND ( a1) AND ( a0); END arc;

16. 모바일컴퓨터특강 16 3x8 Decoder (Signal assignment, Select; Truth Table) LIBRARY ieee; -- 3x8 decoder using vectors USE ieee.std_logic_1164.ALL; -- and selected signal assignment ENTITY decoder_b IS PORT(a: INSTD_LOGIC_VECTOR (2 downto 0); y: OUTSTD_LOGIC_VECTOR (7 downto 0)); END decoder_b ; ARCHITECTURE arc OF decoder_b IS BEGIN WITH a SELECT y<="00000001" WHEN "000", "00000010" WHEN "001", "00000100" WHEN "010", "00001000" WHEN "011", "00010000" WHEN "100", "00100000" WHEN "101", "01000000" WHEN "110", "10000000" WHEN "111", "00000000" WHEN others; END arc;

17. 모바일컴퓨터특강 17 3x8 Decoder with enable LIBRARY ieee; -- 3x8 decoder with enable -- USE ieee.std_logic_1164.ALL; ENTITY decoder_c IS PORT(en: IN std_logic; a: INSTD_LOGIC_VECTOR (2 DOWNTO 0); y: OUTSTD_LOGIC_VECTOR (7 DOWNTO 0)); END decoder_c ; ARCHITECTURE arc OF decoder_c IS SIGNAL inputs : std_logic_vector(3 DOWNTO 0); BEGIN inputs<=en & a; WITH inputs SELECT y<="00000001" WHEN "1000", "00000010" WHEN "1001", "00000100" WHEN "1010", "00001000" WHEN "1011", "00010000" WHEN "1100", "00100000" WHEN "1101", "01000000" WHEN "1110", "10000000" WHEN "1111", "00000000" WHEN others; END arc; concatenat e

18. 모바일컴퓨터특강 18 3x8 Decoder (CASE) (1) library ieee; use ieee.std_logic_1164.all; entity decoder38_proc is port( d2, d1, d0 : in std_logic; y0,y1,y2,y3,y4,y5,y6,y7 : out std_logic); end decoder38_proc; architecture xxx of decoder38_proc is signal d : std_logic_vector(2 downto 0); signal t : std_logic_vector( 0 to 7); begin d <= d2&d1&d0; process(d) begin case d is when "000" => t<="10000000"; when "001" => t<="01000000"; when "010" => t<="00100000"; when "011" => t<="00010000"; when "100" => t<="00001000"; when "101" => t<="00000100"; when "110" => t<="00000010"; when others => t<="00000001"; end case; end process; y0 <= t(0); y1 <= t(1); y2 <= t(2); y3 <= t(3); y4 <= t(4); y5 <= t(5); y6 <= t(6); y7 <= t(7); end xxx; d(2) <= d2; d(1) <= d1; d(0) <= d0; 같은 표현 회로보다는 설계사양에 관심을 둔 설 계방식.

19. 모바일컴퓨터특강 19 Timing Simulation Result 3x8 Decoder (CASE) (2)

20. 모바일컴퓨터특강 20 library ieee; use ieee.std_logic_1164.all; entity mux41_ when is port( a, b, c, d: in std_logic; s : in std_logic_vector(1 downto 0); y : out std_logic); end mux41_ when; architecture a of mux41_when is BEGIN y <= a when (s=“00”) else b when (s=“01”) else c when (s=“10”) else d; END a; Mux 4x1 (Signal Assignment, Conditional)

21. 모바일컴퓨터특강 21 MUX (Multiplexer) 2 N data input, 1 data output, N control inputs that select one of the data inputs. D0 D7 D1 F A B C

22. 모바일컴퓨터특강 22 library ieee; use ieee.std_logic_1164.all; entity mux41_with is port( a, b, c, d: in std_logic; s : in std_logic_vector(1 downto 0); y : out std_logic); end mux41_with; architecture a of mux41_with is BEGIN WITH s SELECT y<= a WHEN "00", b WHEN "01", c WHEN "10", d WHEN others; END a; Mux 4x1 (Signal Assignment, Selected)

23. 모바일컴퓨터특강 23 library ieee; use ieee.std_logic_1164.all; entity mux41_if_proc is port( a,b,c,d : in std_logic; s : in std_logic_vector(1 downto 0); y : out std_logic); end mux41_if_proc; architecture proc of mux41_if_proc is begin process(a,b,c,d,s) begin if( s="00") then y<=a; elsif( s="01") then y<=b; elsif( s="10") then y<=c; else y<=d; end if; end process; end proc; Mux 4x1 (IF)

24. 모바일컴퓨터특강 24 library ieee; use ieee.std_logic_1164.all; entity mux41_case_proc is port( a,b,c,d : in std_logic; s : in std_logic_vector(1 downto 0); y : out std_logic); end mux41_case_proc; architecture proc of mux41_case_proc is begin process(a,b,c,d,s) begin case s is when "00" => y<=a; when "01" => y<=b; when "10" => y<=c; when others => y<=d; end case; end process; end proc; Mux 4x1 (case)

25. 모바일컴퓨터특강 25 Library ieee; Use ieee.std_logic_1164.all; entity mux8_1 is port( a, b, c, d, e, f, g, h : in std_logic; s2, s1, s0 : in std_logic; y : out std_logic); end mux8_1; architecture xxx of mux8_1 is component decoder3_8 port( a, b, c : in std_logic; d0,d1,d2,d3,d4,d5,d6,d7 : out std_logic); end component; signal t : std_logic_vector(7 downto 0); signal d0,d1,d2,d3,d4,d5,d6,d7 : std_logic; begin U1: decoder3_8 port map( s2,s1,s0,d0,d1,d2,d3,d4,d5,d6,d7); t(0) <= a and d0; t(1) <= b and d1; t(2) <= c and d2; t(3) <= d and d3; t(4) <= e and d4; t(5) <= f and d5; t(6) <= g and d6; t(7) <= h and d7; y <= t(0) or t(1) or t(2) or t(3) or t(4) or t(5) or t(6) or t(7); end xxx; t(0) t(1) t(2) t(3) t(4) t(5) t(6) t(7) Decoder3_8.vhd 는 미리 작성된 상태임 Decoder3_8.vhd 는 미리 작성된 상태임 Mixed Modeling : structure + dataflow Mux 8x1 (Mixed Modeling)

26. 모바일컴퓨터특강 26 library ieee; use ieee.std_logic_1164.all; entity mux8_1_proc is port( a,b,c,d,e,f,g,h : in std_logic; s2, s1, s0: in std_logic; y: out std_logic); end mux8_1_proc; architecture proc of mux8_1_proc is constant bits3_0 : std_logic_vector(2 downto 0) := "000"; constant bits3_1 : std_logic_vector(2 downto 0) := "001"; constant bits3_2 : std_logic_vector(2 downto 0) := "010"; constant bits3_3 : std_logic_vector(2 downto 0) := "011"; constant bits3_4 : std_logic_vector(2 downto 0) := "100"; constant bits3_5 : std_logic_vector(2 downto 0) := "101"; constant bits3_6 : std_logic_vector(2 downto 0) := "110"; constant bits3_7 : std_logic_vector(2 downto 0) := "111"; begin process(a,b,c,d,e,f,g,h,s2,s1,s0) variable sel : std_logic_vector(2 downto 0); begin sel := s2 & s1 & s0; case sel is when bits3_0 => y<= a; when bits3_1 => y<= b; when bits3_2 => y<= c; when bits3_3 => y<= d; when bits3_4 => y<= e; when bits3_5 => y<= f; when bits3_6 => y<= g; when others => y<= h; end case; end process; end proc; sel(2) := s2; sel(1) := s1; sel(0) := s0; 같은표현같은표현 같은표현같은표현 Mux 8x1 (Constants)

27. 모바일컴퓨터특강 27 library ieee; use ieee.std_logic_1164.all; entity mux81_4bits_with is port( a, b, c, d, e, f, g, h : in std_logic_vector(3 downto 0); s2, s1, s0 : in std_logic; y : out std_logic_vector(3 downto 0) ); end mux81_4bits_with; architecture a of mux81_4bits_with is signal s : std_logic_vector(2 downto 0); BEGIN s <= s2 & s1 & s0; -- s(2)<=s2; s(1)<=s1;s(0)<=s0; WITH s SELECT y <= a WHEN "000", b WHEN "001", c WHEN "010", d WHEN "011", e WHEN "100", f WHEN "101", g WHEN "110", h WHEN others; END a; Mux 8x14bits (Signal Assignment, Selected)

28. 모바일컴퓨터특강 28 library ieee; use ieee.std_logic_1164.all; entity mux81_4bits_proc is port( a,b,c,d,e,f,g,h : in std_logic_vector(3 downto 0); s2, s1, s0: in std_logic; y: out std_logic_vector(3 downto 0)); end mux81_4bits_proc; architecture proc of mux81_4bits_proc is signal sel : std_logic_vector(2 downto 0); begin sel <= s2 & s1 & s0; process(a,b,c,d,e,f,g,h,sel) begin case sel is when "000" => y<= a; when "001" => y<= b; when "010" => y<= c; when "011" => y<= d; when "100" => y<= e; when "101" => y<= f; when "110" => y<= g; when others => y<= h; end case; end process; end proc; Mux 8x14bits (case)

29. 모바일컴퓨터특강 29 Combinational logic circuits give us many useful devices. One of the simplest is the half adder, which finds the sum of two bits. Based on the truth table, we’ll construct the circuit. Half Adder (1)

30. 모바일컴퓨터특강 30 The sum can be found using the XOR operation and the carry using the AND operation. S = X  Y, C = XY Half Adder (2)

31. 모바일컴퓨터특강 31 Full Adder (1) Full adder adds carry_in as well. The truth table for a full adder is shown at the right.

32. 모바일컴퓨터특강 32 Full Adder (2) - Boolean expression S=  m(1,2,4,7) = X’ Y’ C in + X’ Y C in ’ + X Y’ C in ’ + X Y C in = X’ (Y’ C in + Y C in ’) + X (Y’ C in ’ + Y C in ) = X’ (Y  C in ) + X (Y  C in )’ = X  Y  C in C out =  m(3,5,6,7) = X’ Y C in + X Y’ C in + X Y C in ’ + X Y C in = (X’ Y + X Y’) C in + XY(C in ’ + C in ) = (X  Y) C in + XY

33. 모바일컴퓨터특강 33 Full Adder (3)

34. 모바일컴퓨터특강 34 Full Adder (4) – using Half adder

35. 모바일컴퓨터특강 35 Just as we combined half adders to make a full adder, full adders can be connected in series. The carry bit “ripples” from one adder to the next; hence, this configuration is called a ripple-carry adder. Today’s systems employ more efficient adders. ripple: 잔물결, 파문 Ripple Carry Adder

36. 모바일컴퓨터특강 36 Ripple Carry Adder Operation All 2n input bits available at the same time Carries propagate from the FA in position 0 (with inputs x 0 and y 0 ) to position i before that position produces correct sum and carry-out bits Carries ripple through all n FAs before we can claim that the sum outputs are correct and may be used in further calculations

37. 모바일컴퓨터특강 37 4-bit Adder library ieee; use ieee.std_logic_1164.all; use ieee.std_logic_unsigned.all; entity add_4bits_proc is port( a, b: in std_logic_vector(3 downto 0); s : out std_logic_vector(3 downto 0) ); end add_4bits_proc; architecture a of add_4bits_proc is begin s <= a+b; end a; + 연산자가 사용될 때 꼭 사용. Carry Out 이 16 이므 로 14 를 더 하면 30 이 됨.