How to Represent a Truth Table in VHDL

When working with VHDL (VHSIC Hardware Description Language), you often need to implement circuits based on specific logical operations defined in a truth table. While VHDL itself doesn't have a built-in truth table construct, you can implement the desired logic using conditional statements such as if or case. In this article, we will explore how to represent a truth table using these constructs in VHDL, with examples of a simple 2-input AND gate and a more complex 2-bit binary adder.

Example: 2-input AND Gate Truth Table

Let's start with a basic example of a 2-input AND gate. The truth table for this gate is as follows:

ABOutput 000 010 100 111

The VHDL implementation of this truth table is as follows:

library IEEE;
use _LOGIC_;

entity and_gate is
    Port ( A : in STD_LOGIC;
           B : in STD_LOGIC;
           Y : out STD_LOGIC);
end and_gate;

architecture Behavioral of and_gate is
begin
    process (A, B)
    begin
        if A  '1' and B  '1' then
            Y  '1';
        else
            Y  '0';
        end if;
    end process;
end Behavioral;

Explanation:

Entity Declaration: The entity and_gate defines the inputs A and B and the output Y of the AND gate. Architecture: The architecture Behavioral contains the process that implements the logic. Process Block: Inside the process statement, the conditions based on the values of A and B are checked to determine the output Y.

Using a Case Statement for Complex Truth Tables

For more complex truth tables, using a case statement can simplify the logic. For example, let's consider the implementation of a 2-bit binary adder. The truth table for a binary adder is as follows:

Truth Table for 2-bit Binary Adder

ABCarry InSumCarry Out 000000 001001 010010 011011 100010 101101 110100 111111

The VHDL implementation of this truth table is as follows:

library IEEE;
use _LOGIC_;

entity binary_adder is
    Port ( A : in STD_LOGIC_VECTOR (1 downto 0);
           B : in STD_LOGIC_VECTOR (1 downto 0);
           SUM : out STD_LOGIC_VECTOR (1 downto 0);
           CARRY : out STD_LOGIC);
end binary_adder;

architecture Behavioral of binary_adder is
begin
    process (A, B)
    begin
        case A  B is
            when 00  00 > SUM  00; CARRY  '0';
            when 00  01 > SUM  01; CARRY  '0';
            when 01  00 > SUM  01; CARRY  '0';
            when 01  01 > SUM  10; CARRY  '1';
            when 10  00 > SUM  01; CARRY  '0';
            when 10  01 > SUM  10; CARRY  '1';
            when 11  00 > SUM  10; CARRY  '0';
            when 11  01 > SUM  11; CARRY  '1';
            when 11  11 > SUM  11; CARRY  '1';
            when others > SUM  00; CARRY  '0';
        end case;
    end process;
end Behavioral;

Explanation:

Entity Declaration: The entity binary_adder defines the inputs A and B, and the outputs SUM and CARRY. Architecture: The architecture Behavioral contains the process that implements the logic. Case Statement: The case statement checks the conditions based on the binary inputs A and B to determine the output SUM and CARRY.

Conclusion

By using if statements or case statements within a process in VHDL, you can effectively implement the logic described in a truth table. For more complex functions, you might want to break down the logic into smaller components or use combinational logic constructs such as full adders or lookup tables.