Basic logic functions

    Boolean algebra is at the heart of digital electronics so it is very important to know the functions that operate on base 2 numbers or bits. The term function is used when we discuss functions on paper or in programming, but when designing digital circuits those functions are materialized in logic gates (circuits that perform the basic operations). The circuits I will present have 2 inputs and 1 output but there are variations with more than 2 inputs.

    The AND Function
    This function performs a product so for a 2 input AND gate the output will be input one times input two. The representation of an AND gate is:

    The truth table is:

    

        A  B   O

        0   0    0

        0   1    0

        1   0    0

        1   1    1

    From this table it is clear that the and function is actually a*b. The output will be 1 only when all the inputs are 1. AND is also a minimum function because the output is the minimum value of the inputs or min(A,B).

    The OR function

    OR is a maximum function because the output will have the biggest value of all the inputs. For an n input OR function, if n-1 inputs are 0 and only one is 1 then the output will be 1.

    Representation of an OR gate:

    The truth table is:

        

        A  B   O

        0   0    0

        0   1    1

        1   0    1

        1   1    1

    So we see that the output is 0 only when there isn't a 1 at the input.

    The XOR function

    XOR is short for exclusive OR The output is 1 only when an input is 1 and the other is 0. This function is very useful when detecting parity for example.

    Representation of XOR:

    The truth table is:

        A  B   O

        0   0    0

        0   1    1

        1   0    1

        1   1    0

    Inverter (NOT)

    It is a very important circuit. It takes an input and inverts it's value at the output. So 0 becomes 1 and 1 becomes 0.

    The symbol for the inverter is:

    Other functions

    There are 3 more functions to mention: nand, nor, xnor. These are exactly like and, or, xor but the output is inverted. The symbols are also almost the same. The difference is that these have a small circle at the output side. For example the NAND gate looks like this:

    If you do some project that requires one of these 3 gates but you don't have it, use the non-inverted gate plus an inverter circuit.

    Using all the gates in a project

    Let's make a circuit that takes 2 inputs: a and b. The circuit will have 8 outputs: a and b, a or b, a xor b, a nand b, a nor b, a xnor b, not a, not b. For a and b we will use 2 slide switches and for the outputs 8 LEDs.

    If you don't remember how to use Xilinx ISE you can read my tutorial about starting a project:Link.

    Let's make the entity. It should be like this:

    

    You don't have to use the same names for the entity or I/O of course. Also you can use a 2 element std_logic_vector for the inputs and an 8 element std_logic_vector for the outputs f you want.

    Now it's time to write the code. It should look like this:

    Small reminder: The order in witch you put the statements doesn't count because in the architecture all the statements are concurrent.

    Now you can put in the constraints and implement the project.