Digital Design with Synthesizable VHDL Prof. Stephen A. Edwards Columbia University Spring 2013 Combinational Logic in a Dataflow Style Hierarchy: Instantiating Components (entities) Combinational Logic in a Procedural Style Sequential Logic FSMs Summary of the Three Modeling Styles Ten Commandments of VHDL Writing Testbenches Why HDLs? 1970s: SPICE transistor-level netlists Vdd An XOR built from four NAND gates .MODEL P PMOS .MODEL N NMOS Y .SUBCKT NAND A B Y Vdd Vss M1 Y A Vdd Vdd P A M2 Y B Vdd Vdd P M3 Y A X Vss N B M4 X B Vss Vss N .ENDS Vss X1 A B I1 Vdd 0 NAND X2 A I1 I2 Vdd 0 NAND X3 B I1 I3 Vdd 0 NAND A X2 I2 X4 I2 I3 Y Vdd 0 NAND X1 X4 I1 Y X3 B I3 Why HDLs? 1980s: Graphical schematic capture programs Why HDLs? 1990s: HDLs and Logic Synthesis library ieee; use ieee.std_logic_1164.all; use ieee.numeric_std.all; entity ALU is port(A: in unsigned(1 downto 0); B: in unsigned(1 downto 0); Sel: in unsigned(1 downto 0); Res: out unsigned(1 downto 0)); end ALU; architecture behv of ALU is begin process (A,B,Sel) begin case Sel is when "00" => Res <= A + B; when "01" => Res <= A + (not B) + 1; when "10" => Res <= A and B; when "11" => Res <= A or B; when others => Res <= "XX"; end case; end process; end behv; Two Separate but Equal Languages Verilog and VHDL Verilog: More succinct, less flexible, really messy VHDL: Verbose, very (too?) flexible, fairly messy Part of languages people actually use identical. Every synthesis system supports both. Basic Lexical Rules of VHDL É Free-form: space only separates tokens. É Case-insensitive: “VHDL,” “vHdL,” and “vhdl” are equivalent. É Comments: from “--” to the end of the line. É Identifiers: [a-zA-Z](_?[a-zA-Z0-9])* Examples: X X_or_Y ADDR addr Illegal: 14M CLK__4 FOO_ Literals in VHDL ∗ É Decimal integers : 1 42 153_1203 ∗ É Based integers : 2#1_0010# 16#F001D# É Characters: ’0’ ’1’ ’X’ É Strings: "101011" "XXXXXX" ∗ É Bit string literals : B"1001_0101" X"95" mean "10010101" ∗Underscores added for readability are ignored Combinational Logic in a Dataflow Style Bits Logical True False Binary 1 0 Voltage 1.65–3.3V 0–1.65V Timing Diagram VHDL ’1’ ’0’ In VHDL, zeros and ones on wires are members of an enumerated type. They are not Boolean. The std_logic_1164 package package std_logic_1164 is type std_ulogic is ( ’U’, -- Uninitialized ’X’, -- Forcing Unknown ’0’, -- Forcing0 ’1’, -- Forcing1 ’Z’, -- High Impedance ’W’, -- Weak Unknown ’L’, -- Weak0 ’H’, -- Weak1 ’-’ -- Don’t care ); -- The std_logic type allows tri-state drivers(preferred) subtype std_logic is resolved std_ulogic; -- Lots more... Boolean Operators The basic ones in VHDL: a b a and ba or b not a ’0’ ’0’ ’0’ ’0’ ’1’ ’0’ ’1’ ’0’ ’1’ ’1’ ’1’ ’0’ ’0’ ’1’ ’0’ ’1’ ’1’ ’1’ ’1’ ’0’ a b a nand ba nor ba xor b ’0’ ’0’ ’1’ ’1’ ’0’ ’0’ ’1’ ’1’ ’0’ ’1’ ’1’ ’0’ ’1’ ’0’ ’1’ ’1’ ’1’ ’0’ ’0’ ’0’ Rules of Boolean Algebra (1) -- Precedence not a or b and c = (not a) or (b and c) -- Basic relationships not not a = a a and ’1’ = a a and ’0’ = ’0’ a or ’1’ = ’1’ a or ’0’ = a a and a = a a and not a = ’0’ a or a = a a or not a = ’1’ a nand b = not (a and b) a nor b = not (a or b) a xor ’0’ = a a xor ’1’ = not a a xor b = (not a and b) or (a and not b) Rules of Boolean Algebra (2) -- Commutativity a and b = b and a a or b = b or a -- Associativity a and (b and c) = (a and b) and c a or (b or c) = (a or b) or c -- Distributivity a and (b or c) = a and b or a and c a or (b and c) = (a or b) and (a or c) -- De Morgan’s Law not (a and b) = not a or not b not (a or b) = not a and not b A Full Adder: Truth Table carry <= a b c carry sum (not a and b and c) or ( a and not b and c) or 0 0 0 0 0 ( a and b and not c) or 0 0 1 0 1 ( a and b and c); 0 1 0 0 1 0 1 1 1 0 sum <= 1 0 0 0 1 (not a and not b and c) or 1 0 1 1 0 (not a and b and not c) or 1 1 0 1 0 ( a and not b and not c) or 1 1 1 1 1 ( a and b and c); Each row represents a minterm Sum-of-products form: sum of each minterm in which output is true Simplifying Using Boolean Rules carry <= (not a and b and c) or (a and not b and c) or (a and b and not c) or (a and b and c); <= (a and b and not c) or (a and b and c) or (not a and b and c) or (a and b and c) or (a and not b and c) or (a and b and c); <= (a and b) or (b and c) or (a and c); sum <= (not a and not b and c) or (not a and b and not c) or (a and not b and not c) or (a and b and c); <= (not a) and ((not b and c) or (b and not c)) or a and ((not b and not c) or (b and c)); <= a xor b xor c; Structure of a VHDL Module PROCESS process (clk) PORTS begin if rising_edge(clk) then count <= count + 1; end if; in end process; in DATAFLOW EXPRESSION X <= ’1’ when Y = ’1’ and X = "110"else ’0’ out out SIGNAL inout COMPONENT A Full Adder in VHDL library ieee; -- always needed use ieee.std_logic_1164.all; -- std_logic, et al. entity full_adder is -- the interface port(a, b, c : in std_logic; sum, carry : out std_logic); end full_adder; architecture imp of full_adder is -- the implementation begin sum <= (a xor b) xor c; -- combinational logic carry <= (a and b) or (a and c) or (b and c); end imp; carry c sum c sum b a a carry b ...After Logic Synthesis carry~3 b c carry~0 carry~4 a carry carry~1 sum~1 sum Vectors of Bits Three standard synthesizable bit vector types: Type Library Logic Arith. Neg. std_logic_vector ieee_std_1164 p unsigned numeric_std p p signed numeric_std p p p library ieee; use ieee.std_logic_1164.all; use ieee.numeric_std.all; entity vectors is port(vect : in std_logic_vector(1 downto 0); unsi : in unsigned(7 downto 0); sign : out unsigned(15 downto 0)); end entity; Endianness The perpetual battle: Is “0” most or least significant? Little Endian 3 2 1 0 unsigned(3 downto 0) Big Endian 0 1 2 3 unsigned(0 to 3) Arguments on both sides will continue forever. I suggest using Little Endian for vectors. Binary and Hexadecimal in VHDL Dec. Binary Hex 0 "0" x"0" 1 "1" x"1" Vector types are arrays of 2 "10" x"2" 3 "11" x"3" std_logic 4 "100" x"4" 5 "101" x"5" Literals are therefore strings of 0’s 6 "110" x"6" and 1’s 7 "111" x"7" 8 "1000" x"8" -- from std_logic_1164 9 "1001" x"9" type std_logic_vector is 10 "1010" x"A" array (natural range <>) of std_logic; 11 "1011" x"B" 12 "1100" x"C" --- from numeric_std 13 "1101" x"D" type unsigned is 14 "1110" x"E" array (natural range <>) of std_logic; 15 "1111" x"F" 16 "10000" x"10" type signed is 17 "10001" x"11" array (natural range <>) of std_logic; 18 "10010" x"12" 19 "10011" x"13" Two’s Complement Dec. Binary Hex How do you represent negative -8 "1000" x"8" numbers? -7 "1001" x"9" -6 "1010" x"A" Two’s complement produces simpler -5 "1011" x"B" -4 "1100" x"C" logic than sign bit alone. -3 "1101" x"D" n -2 "1110" x"E" Idea: Add constant 2 to negative -1 "1111" x"F" numbers. Simply discard overflow 0 "0000" x"0" after addition or subtraction. 1 "0001" x"1" 2 "0010" x"2" n 1 An n-bit number represents 2 − 3 "0011" x"3" n 1 − 4 "0100" x"4" to 2 − 1. 5 "0101" x"5" − 6 "0110" x"6" The signed type in numeric_std 7 "0111" x"7" uses this A Hex-to-seven-segment Decoder a f b g e c d VHDL: Hex-to-7-segment Decoder library ieee; use ieee.std_logic_1164.all; use ieee.numeric_std.all; -- Provides the unsigned type entity hex7seg is port ( input : in unsigned(3 downto 0); --A number output : out std_logic_vector(6 downto 0)); -- Just bits end hex7seg; architecture combinational of hex7seg is begin with input select output <= "0111111" when x"0", "0000110" when x"1", -- Bad style "1011011" when x"2", "1001111" when x"3", -- one case "1100110" when x"4", "1101101" when x"5", -- per line "1111101" when x"6", "0000111" when x"7", -- preferred "1111111" when x"8", "1101111" when x"9", "1110111" when x"A", "1111100" when x"B", "0111001" when x"C", "1011110" when x"D", "1111001" when x"E", "1110001" when x"F", "XXXXXXX" when others; end combinational; Four-to-one mux: when .. else library ieee; use ieee.std_logic_1164.all; use ieee.numeric_std.all; entity multiplexer_4_1 is port(in0, in1, in2, in3 : in unsigned(15 downto 0); s : in unsigned(1 downto 0); z : out unsigned(15 downto 0)); end multiplexer_4_1; architecture comb of multiplexer_4_1 is begin z <= in0 when s = "00" else in1 when s = "01" else in2 when s = "10" else in3 when s = "11" else (others => ’X’); -- Shorthand for"allX’s" end comb; Four-to-one mux: with...select library ieee; use ieee.std_logic_1164.all; use ieee.numeric_std.all; entity multiplexer_4_1 is port(in0, in1, in2, in3 : in unsigned(15 downto 0); s0, s1 : in std_logic; z : out unsigned(15 downto 0)); end multiplexer_4_1; architecture comb of multiplexer_4_1 is signal sels : unsigned(1 downto 0); begin sels <= s1 & s0; -- "&" is vector concatenation with sels select -- would not resolve type if"s1& s0" here z <= in0 when "00", in1 when "01", in2 when "10", in3 when "11", (others => ’X’) when others; end comb; Three-to-eight Decoder library ieee; use ieee.std_logic_1164.all; use ieee.numeric_std.all; entity dec1_8 is port ( sel : in unsigned(2 downto 0); res : out unsigned(7 downto 0)); end dec1_8; architecture comb of dec1_8 is begin res <= "00000001" when sel = "000" else "00000010" when sel = "001" else "00000100" when sel = "010" else "00001000" when sel = "011" else "00010000" when sel = "100" else "00100000" when sel = "101" else "01000000" when sel = "110" else "10000000"; end comb; Priority Encoder library ieee; use ieee.std_logic_1164.all; use ieee.numeric_std.all; entity priority is port ( sel : in std_logic_vector(7 downto 0); code : out unsigned(2 downto 0)); end priority; architecture imp of priority is begin code <= "000" when sel(0) = ’1’ else "001" when sel(1) = ’1’ else "010" when