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CS/EE 3700 : Fundamentals of Digital System Design

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CS/EE 3700 : Fundamentals of Digital System Design. Chris J. Myers Lecture 10: Digital System Design Chapter 10. Digital System Design. Digital system consists of two parts: Datapath circuit – used to store, manipulate, and transfer date.

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  1. CS/EE 3700 : Fundamentals of Digital System Design Chris J. Myers Lecture 10: Digital System Design Chapter 10

  2. Digital System Design • Digital system consists of two parts: • Datapath circuit – used to store, manipulate, and transfer date. • Control circuit – controls the operation of the datapath. Usually its built using an FSM.

  3. E 0 Q Q D R 1 Clock Q Figure 10.1 A flip-flop with an enable input

  4. LIBRARY ieee ; USE ieee.std_logic_1164.all ; ENTITY rege IS PORT ( R, Resetn, E, Clock : IN STD_LOGIC ; Q : BUFFER STD_LOGIC ) ; END rege ; ARCHITECTURE Behavior OF rege IS BEGIN PROCESS ( Resetn, Clock ) BEGIN IF Resetn = '0' THEN Q <= '0' ; ELSIF Clock'EVENT AND Clock = '1' THEN IF E = '1' THEN Q <= R ; ELSE Q <= Q ; END IF ; END IF ; END PROCESS ; END Behavior ; Figure 10.2 VHDL code for a D flip-flop with an enable input

  5. LIBRARY ieee ; USE ieee.std_logic_1164.all ; ENTITY regne IS GENERIC ( N : INTEGER := 4 ) ; PORT ( R : IN STD_LOGIC_VECTOR(N-1 DOWNTO 0) ; Resetn : IN STD_LOGIC ; E, Clock : IN STD_LOGIC ; Q : OUT STD_LOGIC_VECTOR(N-1 DOWNTO 0) ) ; END regne ; ARCHITECTURE Behavior OF regne IS BEGIN PROCESS ( Resetn, Clock ) BEGIN IF Resetn = '0' THEN Q <= (OTHERS => '0') ; ELSIF Clock'EVENT AND Clock = '1' THEN IF E = '1' THEN Q <= R ; END IF ; END IF ; END PROCESS ; END Behavior ; Figure 10.3 VHDL code for an n-bit register with an enable input

  6. LIBRARY ieee ; USE ieee.std_logic_1164.all ; -- right-to-left shift register with parallel load and enable ENTITY shiftlne IS GENERIC ( N : INTEGER := 4 ) ; PORT( R : IN STD_LOGIC_VECTOR(N-1 DOWNTO 0) ; L, E, w : IN STD_LOGIC ; Clock : IN STD_LOGIC ; Q : BUFFER STD_LOGIC_VECTOR(N-1 DOWNTO 0) ) ; END shiftlne ; ARCHITECTURE Behavior OF shiftlne IS BEGIN PROCESS BEGIN … con’t Figure 10.4a Code for a right-to-left shift register with an enable input

  7. … con’t WAIT UNTIL Clock'EVENT AND Clock = '1' ; IF E = '1' THEN IF L = '1' THEN Q <= R ; ELSE Q(0) <= w ; Genbits: FOR i IN 1 TO N-1 LOOP Q(i) <= Q(i-1) ; END LOOP ; END IF ; END IF ; END PROCESS ; END Behavior ; Figure 10.4b Code for a right-to-left shift register with an enable input (con’t)

  8. LIBRARY ieee ; USE ieee.std_logic_1164.all ; PACKAGE components IS -- 2-to-1 multiplexer COMPONENT mux2to1 PORT ( w0, w1 : IN STD_LOGIC ; s : IN STD_LOGIC ; f : OUT STD_LOGIC ) ; END COMPONENT ; -- D flip-flop with 2-to-1 multiplexer connected to D COMPONENT muxdff PORT ( D0, D1, Sel, Clock : IN STD_LOGIC ; Q : OUT STD_LOGIC ) ; END COMPONENT ; -- n-bit register with enable COMPONENT regne GENERIC ( N : INTEGER := 4 ) ; PORT ( R : IN STD_LOGIC_VECTOR(N-1 DOWNTO 0) ; Resetn : IN STD_LOGIC ; E, Clock : IN STD_LOGIC ; Q : OUT STD_LOGIC_VECTOR(N-1 DOWNTO 0) ) ; END COMPONENT ; … con’t Figure 10.5a Component declaration statements for building blocks

  9. … con’t -- n-bit right-to-left shift register with parallel load and enable COMPONENT shiftlne GENERIC ( N : INTEGER := 4 ) ; PORT ( R : IN STD_LOGIC_VECTOR(N-1 DOWNTO 0) ; L, E, w : IN STD_LOGIC ; Clock : IN STD_LOGIC ; Q : BUFFER STD_LOGIC_VECTOR(N-1 DOWNTO 0) ) ; END COMPONENT ; -- n-bit left-to-right shift register with parallel load and enable COMPONENT shiftrne GENERIC ( N : INTEGER := 4 ) ; PORT ( R : IN STD_LOGIC_VECTOR(N-1 DOWNTO 0) ; L, E, w : IN STD_LOGIC ; Clock : IN STD_LOGIC ; Q : BUFFER STD_LOGIC_VECTOR(N-1 DOWNTO 0) ) ; END COMPONENT ; … con’t Figure 10.5b Component declaration statements for building blocks (con’t)

  10. … con’t -- up-counter that counts from 0 to modulus-1 COMPONENT upcount GENERIC ( modulus : INTEGER := 8 ) ; PORT ( Resetn : IN STD_LOGIC ; Clock, E, L : IN STD_LOGIC ; R : IN INTEGER RANGE 0 TO modulus-1 ; Q : BUFFER INTEGER RANGE 0 TO modulus-1 ) ; END COMPONENT ; -- down-counter that counts from modulus-1 down to 0 COMPONENT downcnt GENERIC ( modulus : INTEGER := 8 ) ; PORT ( Clock, E, L : IN STD_LOGIC ; Q : BUFFER INTEGER RANGE 0 TO modulus-1 ) ; END COMPONENT ; END components ; Figure 10.5c Component declaration statements for building blocks (con’t)

  11. Static Random Access Memory • SRAM is used when a large amount of data needs to be stored. • SRAM block is 2-dimensional array of SRAM cells where each cell stores 1-bit. • To store m elements of n-bits, the aspect ratio of the SRAM array would be mn.

  12. Sel Data Data Figure 10.6 An SRAM cell

  13. Data Data 1 0 Sel 0 Sel 1 Figure 10.7 A 2 x 2 array of SRAM cells

  14. d d d Data inputs n – 1 n – 2 0 Write Sel 0 Sel 1 Sel a 2 0 decoder a 1 m Address -to-2 a m m – 1 Sel m 2 ” 1 Read q q q Data outputs n – 1 n – 2 0 Figure 10.8 A 2mxn SRAM block

  15. B = 0 ; while A  0 do a = 1 if then 0 B = B + 1 ; End if; A Right-shift ; End while; Figure 10.9 Pseudo-code for the bit counter

  16. Reset S1 ¬ B 0 Load A 0 0 1 s s 1 S2 S3 Shift right A Done 1 ¬ A = 0 ? B B + 1 0 0 a 0 1 Figure 10.10 ASM chart for the bit counter

  17. 0 Data log n n 2 w 0 LB L L Counter LA EB E Shift E EA Clock log n A 2 n z B a 0 Figure 10.11 Data path for the bit counter

  18. Reset S1 , LB EB EA 0 0 1 0 1 LA s s 1 S2 S3 Done EA 1 z EB 0 0 a 0 1 Figure 10.12 ASM chart for the bit counter control circuit

  19. LIBRARY ieee ; USE ieee.std_logic_1164.all ; LIBRARY work ; USE work.components.shiftrne ; ENTITY bitcount IS PORT( Clock, Resetn : IN STD_LOGIC ; LA, s : IN STD_LOGIC ; Data : IN STD_LOGIC_VECTOR(7 DOWNTO 0) ; B : BUFFER INTEGER RANGE 0 to 8 ; Done : OUT STD_LOGIC ) ; END bitcount ; ARCHITECTURE Behavior OF bitcount IS TYPE State_type IS ( S1, S2, S3 ) ; SIGNAL y : State_type ; SIGNAL A : STD_LOGIC_VECTOR(7 DOWNTO 0) ; SIGNAL z, EA, LB, EB, low : STD_LOGIC ; BEGIN FSM_transitions: PROCESS ( Resetn, Clock ) BEGIN IF Resetn = '0' THEN y <= S1 ; … con’t Figure 10.13a VHDL code for the bit-counting circuit

  20. ELSIF (Clock'EVENT AND Clock = '1') THEN CASE y IS WHEN S1 => IF s = '0' THEN y <= S1 ; ELSE y <= S2 ; END IF ; WHEN S2 => IF z = '0' THEN y <= S2 ; ELSE y <= S3 ; END IF ; WHEN S3 => IF s = '1' THEN y <= S3 ; ELSE y <= S1 ; END IF ; END CASE ; END IF ; END PROCESS ; FSM_outputs: PROCESS ( y, s, A(0), z ) BEGIN EA <= '0' ; LB <= '0' ; EB <= '0' ; Done <= '0' ; CASE y IS WHEN S1 => LB <= '1' ; EB <= '1' ; IF s = '0' AND LA = '1' THEN EA <= '1' ; ELSE EA <= '0' ; END IF ; WHEN S2 => EA <= '1' ; IF A(0) = '1' THEN EB <= '1' ; ELSE EB <= '0' ; END IF ; … con’t Figure 10.13b VHDL code for the bit-counting circuit (con’t)

  21. WHEN S3 => Done <= '1' ; END CASE ; END PROCESS ; -- The datapath circuit is described below upcount: PROCESS ( Resetn, Clock ) BEGIN IF Resetn = '0' THEN B <= 0 ; ELSIF (Clock'EVENT AND Clock = '1') THEN IF EB = '1' THEN IF LB = '1' THEN B <= 0 ; ELSE B <= B + 1 ; END IF ; END IF ; END IF; END PROCESS; low <= '0' ; ShiftA: shiftrne GENERIC MAP ( N => 8 ) PORT MAP ( Data, LA, EA, low, Clock, A ) ; z <= '1' WHEN A = "00000000" ELSE '0' ; END Behavior ; Figure 10.13c VHDL code for the bit-counting circuit (con’t)

  22. Figure 10.14 Simulation results for the bit-counting circuit

  23. P = 0 ; – i = 0 n 1 for to do b = 1 if then i P = P + A ; end if; A Left-shift ; end for; Decimal Binary 13 1 1 0 1 Multiplicand 11 1 0 1 1 Multiplier ´ ´ 13 1 1 0 1 13 1 1 0 1 0 0 0 0 143 1 1 0 1 1 0 0 0 1 1 1 1 Product (a) Manual method (b) Pseudo-code Figure 10.15 An algorithm for multiplication

  24. Reset S1 ¬ P 0 Load A Load B 0 0 1 s s 1 S2 S3 Shift left A , Shift right B Done 1 ¬ B = 0 ? P P + A 0 0 b 0 1 Figure 10.16 ASM chart for the multiplier

  25. LA 0 DataA LB DataB n n n L L Shift-left Shift-right EA EB E E register register A B Clock n 2n + z b Sum 0 0 2n 2n 1 0 Psel 2n DataP EP E Register 2n P Figure 10.17 Datapath circuit for the multiplier

  26. Reset S1 , = 0 EP Psel 0 0 0 LB LA s 1 1 1 EB EA 0 1 s S3 S2 , , = 1 EAEB Done Psel 1 z EP 0 0 b 0 1 Figure 10.18 ASM chart for the multiplier control circuit

  27. LIBRARY ieee ; USE ieee.std_logic_1164.all ; USE ieee.std_logic_unsigned.all ; USE work.components.all ; ENTITY multiply IS GENERIC ( N : INTEGER := 8; NN : INTEGER := 16 ) ; PORT ( Clock : IN STD_LOGIC ; Resetn : IN STD_LOGIC ; LA, LB, s : IN STD_LOGIC ; DataA : IN STD_LOGIC_VECTOR(N-1 DOWNTO 0) ; DataB : IN STD_LOGIC_VECTOR(N-1 DOWNTO 0) ; P : BUFFER STD_LOGIC_VECTOR(NN-1 DOWNTO 0) ; Done : OUT STD_LOGIC ) ; END multiply ; ARCHITECTURE Behavior OF multiply IS TYPE State_type IS ( S1, S2, S3 ) ; SIGNAL y : State_type ; SIGNAL Psel, z, EA, EB, EP, Zero : STD_LOGIC ; SIGNAL B, N_Zeros : STD_LOGIC_VECTOR(N-1 DOWNTO 0) ; SIGNAL A, Ain, DataP, Sum : STD_LOGIC_VECTOR(NN-1 DOWNTO 0) ; BEGIN … con’t Figure 10.19a VHDL code for the multiplier circuit

  28. FSM_transitions: PROCESS ( Resetn, Clock ) BEGIN IF Resetn = '0' THEN y <= S1 ; ELSIF (Clock'EVENT AND Clock = '1') THEN CASE y IS WHEN S1 => IF s = '0' THEN y <= S1 ; ELSE y <= S2 ; END IF ; WHEN S2 => IF z = '0' THEN y <= S2 ; ELSE y <= S3 ; END IF ; WHEN S3 => IF s = '1' THEN y <= S3 ; ELSE y <= S1 ; END IF ; END CASE ; END IF ; END PROCESS ; FSM_outputs: PROCESS ( y, s, LA, LB, B(0) ) BEGIN EP <= '0' ; EA <= '0' ; EB <= '0' ; Done <= '0' ; Psel <= '0'; CASE y IS WHEN S1 => EP <= '1' ; IF s = '0' AND LA = '1' THEN EA <= '1' ; ELSE EA <= '0' ; END IF ; IF s = '0' AND LB = '1' THEN EB <= '1' ; … con’t Figure 10.19b VHDL code for the multiplier circuit (con’t)

  29. ELSE EB <= '0' ; END IF ; WHEN S2 => EA <= '1' ; EB <= '1' ; Psel <= '1' ; IF B(0) = '1' THEN EP <= '1' ; ELSE EP <= '0' ; END IF ; WHEN S3 => Done <= '1' ; END CASE ; END PROCESS ; -- Define the datapath circuit Zero <= '0' ; N_Zeros <= (OTHERS => '0' ) ; Ain <= N_Zeros & DataA ; ShiftA: shiftlne GENERIC MAP ( N => NN ) PORT MAP ( Ain, LA, EA, Zero, Clock, A ) ; ShiftB: shiftrne GENERIC MAP ( N => N ) PORT MAP ( DataB, LB, EB, Zero, Clock, B ) ; z <= '1' WHEN B = N_Zeros ELSE '0' ; Sum <= A + P ; -- Define the 2n 2-to-1 multiplexers for DataP GenMUX: FOR i IN 0 TO NN-1 GENERATE Muxi: mux2to1 PORT MAP ( Zero, Sum(i), Psel, DataP(i) ) ; END GENERATE; RegP: regne GENERIC MAP ( N => NN ) PORT MAP ( DataP, Resetn, EP, Clock, P ) ; END Behavior ; Figure 10.19c VHDL code for the multiplier circuit (con’t)

  30. Figure 10.20 Simulation results for the multiplier circuit

  31. 15 Q 00001111 9 140 A 1001 100 01100 B 9 1001 50 10 001 45 10 01 10000 5 1001 1110 1001 (a) An example using decimal numbers R 101 (b) Using binary numbers R = 0 ; i = 0 n – 1 for to do R A Left-shift ;  if R B then q = 1 ; i – R = R B ; else q = 0 ; i end if; end for; (c) Pseudo-code Figure 10.21 An algorithm for division

  32. Reset S1 ¬ , ¬ R 0 C n 1 – Load A Load B 0 1 s 0 1 S2 s Shift left R||A S4 S3 ¬ C C ” 1 Done 0 1 ³ R B ? Shift 1 into Q Shift 0 into Q ¬ R R B – 1 0 C = 0 ? Figure 10.22 ASM chart for the divider

  33. 0 n DataB DataA LA EB Rsel 1 0 n n LR L E L Left-shift Left-shift Register E w ER EA register register E n n n B a n ” 1 A EQ E Left-shift c c w 1 out in register + n n Clock Q R Figure 10.23 Datapath circuit for the divider

  34. Reset S1 EA , = 0 Rsel LR, ER, LC, EC 1 0 1 0 LA s S2 ER, EA S3 , = 1 EC EQ, Rsel 0 1 0 c s out 1 S4 Done LR, ER 1 0 z Figure 10.24 ASM chart for the divider control circuit

  35. B 1001 10001100 A rr Clock cycle R A/ Q 0 Load A, B 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 Shift left 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 , ¬ 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 Shift left Q 0 1 0 , 0 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 ¬ 2 Shift left Q 0 0 , 0 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 ¬ 3 Shift left Q 0 0 , ¬ 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 Shift left Q 0 4 0 , ¬ 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 1 Subtract Q 1 5 0 , ¬ 6 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 Subtract Q 1 0 , ¬ Subtract Q 1 7 0 0 1 1 0 0 0 1 1 1 0 0 0 1 0 0 0 0 , ¬ Subtract Q 1 8 0 0 0 1 0 1 0 0 0 0 1 1 1 1 0 0 0 0 Figure 10.25 An example of division using n = 8 clock cycles

  36. Reset S1 , , , = 0 LC EC ER Rsel EA 1 1 0 s LA 0 EA, ER0 LR S2 , , , ER ER0 EA = 1 Rsel 0 0 1 c s out 1 S3 LR EC Done 1 0 z Figure 10.26 An example of division using n = 8 clock cycles

  37. DataB LA DataA EB n n L E Left-shift Register EA w E register Clock n n B c c 1 out in + n 0 n Rsel 1 0 ER0 rr LR L 0 0 0 Left-shift ER w E Q D register 1 q n – 1 Q n n n – 1 ¼ r r n – 2 0 n n Q R Figure 10.27 Datapath circuit for the enhanced divider

  38. LIBRARY ieee; USE ieee.std_logic_1164.all; USE ieee.std_logic_unsigned.all ; USE work.components.all ; ENTITY divider IS GENERIC ( N : INTEGER := 8 ) ; PORT ( Clock : IN STD_LOGIC ; Resetn : IN STD_LOGIC ; s, LA, EB : IN STD_LOGIC ; DataA : IN STD_LOGIC_VECTOR(N-1 DOWNTO 0) ; DataB : IN STD_LOGIC_VECTOR(N-1 DOWNTO 0) ; R, Q : BUFFER STD_LOGIC_VECTOR(N-1 DOWNTO 0) ; Done : OUT STD_LOGIC ) ; END divider ; ARCHITECTURE Behavior OF divider IS TYPE State_type IS ( S1, S2, S3 ) ; SIGNAL y : State_type ; SIGNAL Zero, Cout, z : STD_LOGIC ; SIGNAL EA, Rsel, LR, ER, ER0, LC, EC, R0 : STD_LOGIC ; SIGNAL A, B, DataR : STD_LOGIC_VECTOR(N-1 DOWNTO 0) ; SIGNAL Sum : STD_LOGIC_VECTOR(N DOWNTO 0) ; -- adder outputs SIGNAL Count : INTEGER RANGE 0 TO N-1 ; … con’t Figure 10.28a VHDL code for the divider circuit

  39. BEGIN FSM_transitions: PROCESS ( Resetn, Clock ) BEGIN IF Resetn = '0' THEN y <= S1 ; ELSIF (Clock'EVENT AND Clock = '1') THEN CASE y IS WHEN S1 => IF s = '0' THEN y <= S1 ; ELSE y <= S2 ; END IF ; WHEN S2 => IF z = '0' THEN y <= S2 ; ELSE y <= S3 ; END IF ; WHEN S3 => IF s = '1' THEN y <= S3 ; ELSE y <= S1 ; END IF ; END CASE ; END IF ; END PROCESS ; FSM_outputs: PROCESS ( s, y, Cout, z ) BEGIN LR <= '0' ; ER <= '0' ; ER0 <= '0' ; LC <= '0' ; EC <= '0' ; EA <= '0' ; Done <= '0' ; Rsel <= '0' ; CASE y IS WHEN S1 => … con’t Figure 10.28b VHDL code for the divider circuit (con’t)

  40. LC <= '1' ; EC <= '1' ; ER <= '1' ; IF s = '0' THEN LR <= '1' ; IF LA = '1' THEN EA <= '1' ; ELSE EA <= '0' ; END IF ; ELSE EA <= '1' ; ER0 <= '1' ; END IF ; WHEN S2 => Rsel <= '1' ; ER <= '1' ; ER0 <= '1' ; EA <= '1' ; IF Cout = '1' THEN LR <= '1' ; ELSE LR <= '0' ; END IF ; IF z = '0' THEN EC <= '1' ; ELSE EC <= '0' ; END IF ; WHEN S3 => Done <= '1' ; END CASE ; END PROCESS ; -- define the datapath circuit Zero <= '0' ; RegB: regne GENERIC MAP ( N => N ) PORT MAP ( DataB, Resetn, EB, Clock, B ) ; ShiftR: shiftlne GENERIC MAP ( N => N ) PORT MAP ( DataR, LR, ER, R0, Clock, R ) ; … con’t Figure 10.28c VHDL code for the divider circuit (con’t)

  41. FF_R0: muxdff PORT MAP ( Zero, A(N-1), ER0, Clock, R0 ) ; ShiftA: shiftlne GENERIC MAP ( N => N ) PORT MAP ( DataA, LA, EA, Cout, Clock, A ) ; Q <= A ; Counter: downcnt GENERIC MAP ( modulus => N ) PORT MAP ( Clock, EC, LC, Count ) ; z <= '1' WHEN Count = 0 ELSE '0' ; Sum <= R & R0 + (NOT B +1) ; Cout <= Sum(N) ; DataR <= (OTHERS => '0') WHEN Rsel = '0' ELSE Sum ; END Behavior ; Figure 10.28d VHDL code for the divider circuit (con’t)

  42. Figure 10.29 Simulation results for the divider circuit

  43. = 0 Sum ; – i = k 1 for down to 0 do = +R ; Sum Sum i end for; = ÷ k M Sum ; (a) Pseudo-code Reset S1 Sum 0 ¬ , ¬ C k – 1 Load registers 0 s 1 S2 ¬ Sum Sum + R i ¬ C C – 1 0 0 C = 0 ? s 1 1 S3 S4 ¬ ¤ M Sum k Done (b) ASM chart Figure 10.30 An algorithm for finding the mean of k numbers

  44. Figure 10.31 Datapath circuit for the mean operation

  45. Figure 10.32 ASM chart for the control circuit

  46. Figure 10.33 Schematic of the mean circuit with an SRAM block

  47. Figure 10.34 Simulation results for the mean circuit using SRAM

  48. – i = 0 k 2 for to do A = R ; i – j = i + 1 k 1 for to do B = R ; j B < A if then R = B ; i R = A ; j A = R ; i end if ; end for; end for; Figure 10.35 Pseudo-code for the sort operation

  49. Reset S1 ¬ 0 C i Load registers 0 s 1 S2 ¬ , ¬ A R C C i j i S3 ¬ C C + 1 ¬ C C + 1 j j i i S4 ¬ B R j S5 S6 1 ¬ C C + 1 ¬ R A B < A ? j j j 0 S7 ¬ R B i S8 ¬ A R i 0 C = k – 1 ? j S9 0 1 Done s 1 1 0 C = k – 2 ? i Figure 10.36 ASM chart for the sort operation

  50. DataIn ABmux n WrInit 0 1 n RData Rin Rin Rin Rin E E E E 0 1 2 3 R R R R 0 1 2 3 0 1 2 3 Imux ABData Ain Bin Rd E E n Clock DataOut < Bout 1 0 A B BltA Figure 10.37 A part of the datapath circuit for the sort operation