VHDL Logical Operators and Signal Assignments for Combinational Logic

By John
May 16, 2020

In this post, we discuss the VHDL logical operators, when-else statements, with-select statements and instantiation. These basic techniques allow us to model simple digital circuits.

In a previous post in this series, we looked at the way we use the VHDL entity, architecture and library keywords. These are important concepts which provide structure to our code and allow us to define the inputs and outputs of a component.

However, we can't do anything more than define inputs and outputs using this technique. In order to model digital circuits in VHDL, we need to take a closer look at the syntax of the language.

There are two main classes of digital circuit we can model in VHDL – combinational and sequential.

Combinational logic is the simplest of the two, consisting primarily of basic logic gates, such as ANDs, ORs and NOTs. When the circuit input changes, the output changes almost immediately (there is a small delay as signals propagate through the circuit).

Sequential circuits use a clock and require storage elements such as flip flops. As a result, changes in the output are synchronised to the circuit clock and are not immediate. We talk more specifically about modelling combinational logic in this post, whilst sequential logic is discussed in the next post.

Combinational Logic

The simplest elements to model in VHDL are the basic logic gates – AND, OR, NOR, NAND, NOT and XOR.

Each of these type of gates has a corresponding operator which implements their functionality. Collectively, these are known as logical operators in VHDL.

To demonstrate this concept, let us consider a simple two input AND gate such as that shown below.

A 2 input and gate.

The VHDL code shown below uses one of the logical operators to implement this basic circuit.

and_out <= a and b;

Although this code is simple, there are a couple of important concepts to consider. The first of these is the VHDL assignment operator (<=) which must be used for all signals. This is roughly equivalent to the = operator in most other programming languages.

In addition to signals, we can also define variables which we use inside of processes. In this case, we would have to use a different assignment operator (:=).

It is not important to understand variables in any detail to model combinational logic but we talk about them in the post on the VHDL process block.

The type of signal used is another important consideration. We talked about the most basic and common VHDL data types in a previous post.

As they represent some quantity or number, types such as real, time or integer are known as scalar types. We can't use the VHDL logical operators with these types and we most commonly use them with std_logic or std_logic_vectors.

Despite these considerations, this code example demonstrates how simple it is to model basic logic gates.

We can change the functionality of this circuit by replacing the AND operator with one of the other VHDL logical operators.

As an example, the VHDL code below models a three input XOR gate.

or_out <= a xor b xor c;

The NOT operator is slightly different to the other VHDL logical operators as it only has one input. The code snippet below shows the basic syntax for a NOT gate.

not_out <= not a;

Mixing VHDL Logical Operators

Combinational logic circuits almost always feature more than one type of gate. As a result of this, VHDL allows us to mix logical operators in order to create models of more complex circuits.

To demonstrate this concept, let’s consider a circuit featuring an AND gate and an OR gate. The circuit diagram below shows this circuit.

A logic circuit with the function (a and b) or c.

The code below shows the implementation of this circuit using VHDL.

logic_out <= (A and B) or C;

This code should be easy to understand as it makes use of the logical operators we have already talked about. However, it is important to use brackets when modelling circuits with multiple logic gates, as shown in the above example. Not only does this ensure that the design works as intended, it also makes the intention of the code easier to understand.

Reduction Functions

We can also use the logical operators on vector types in order to reduce them to a single bit. This is a useful feature as we can determine when all the bits in a vector are either 1 or 0.

We commonly do this for counters where we may want to know when the count reaches its maximum or minimum value.

The logical reduction functions were only introduced in VHDL-2008. Therefore, we can not use the logical operators to reduce vector types to a single bit when working with earlier standards.

The code snippet below shows the most common use cases for the VHDL reduction functions.

-- Using a nor to determine when a vector is 0
example <= nor( <std_logic_vector> );
-- Using an and to determine when a vector is all 1
example <= and( <std_logic_vector> );

Mulitplexors in VHDL

In addition to logic gates, we often use multiplexors (mux for short) in combinational digital circuits. In VHDL, there are two different concurrent statements which we can use to model a mux.

The VHDL with select statement, also commonly referred to as selected signal assignment, is one of these constructs.

The other method we can use to concurrently model a mux is the VHDL when else statement.

In addition to this, we can also use a case statement to model a mux in VHDL. However, we talk about this in more detail in a later post as this method also requires us to have an understanding of the VHDL process block.

Let's look at the VHDL concurrent statements we can use to model a mux in more detail.

VHDL With Select Statement

When we use the with select statement in a VHDL design, we can assign different values to a signal based on the value of some other signal in our design.

The with select statement is probably the most intuitive way of modelling a mux in VHDL.

The code snippet below shows the basic syntax for the with select statement in VHDL.

with <address> select <mux_out> <=
  <a> when <address1>,
  <b> when <address2>,
  <c> when others;

When we use the VHDL with select statement, the <mux_out> field is assigned data based on the value of the <address> field.

When the <address> field is equal to <address1> then the <mux_out> signal is assigned to <a>, for example.

We use the the others clause at the end of the statement to capture instance when the address is a value other than those explicitly listed.

We can exclude the others clause if we explicitly list all of the possible input combinations.

With Select Mux Example

Let’s consider a simple four to one multiplexer to give a practical example of the with select statement. The output Q is set to one of the four inputs (A,B, C or D) depending on the value of the addr input signal.

The circuit diagram below shows this circuit.

A four input multiplexor

This circuit is simple to implement using the VHDL with select statement, as shown in the code snippet below.

with addr select q <=
  a when "00",
  b when "01",
  c when "10",
  d when others;

VHDL When Else Statements

We use the when statement in VHDL to assign different values to a signal based on boolean expressions.

In this case, we actually write a different expression for each of the values which could be assigned to a signal. When one of these conditions evaluates as true, the signal is assigned the value associated with this condition.

The code snippet below shows the basic syntax for the VHDL when else statement.

<mux_out> <= <a> when <address> = <address1>
  else <b> when <address> = <address2>
  else <c>;

When we use the when else statement in VHDL, the boolean expression is written after the when keyword. If this condition evaluates as true, then the <mux_out> field is assigned to the value stated before the relevant when keyword.

For example, if the <address> field in the above example is equal to <address1> then the value of <a> is assigned to <mux_out>.

When this condition evaluates as false, the next condition in the sequence is evaluated.

We use the else keyword to separate the different conditions and assignments in our code.

The final else statement captures the instances when the address is a value other than those explicitly listed. We only use this if we haven't explicitly listed all possible combinations of the <address> field.

When Else Mux Example

Let’s consider the simple four to one multiplexer again in order to give a practical example of the when else statement in VHDL. The output Q is set to one of the four inputs (A,B, C or D) based on the value of the addr signal. This is exactly the same as the previous example we used for the with select statement.

The VHDL code shown below implements this circuit using the when else statement.

q <= a when addr = "00"
  else b when addr = "01"
  else c when addr = "10"
  else d;

Comparison of Mux Modelling Techniques in VHDL

When we write VHDL code, the with select and when else statements perform the same function. In addition, we will get the same synthesis results from both statements in almost all cases.

In a purely technical sense, there is no major advantage to using one over the other. The choice of which one to use is often a purely stylistic choice.

When we use the with select statement, we can only use a single signal to determine which data will get assigned.

This is in contrast to the when else statements which can also include logical descriptors.

This means we can often write more succinct VHDL code by using the when else statement. This is especially true when we need to use a logic circuit to drive the address bits.

Let's consider the circuit shown below as an example.

A 2 input multiplexor circuit. The address bit of the multiplexor are being driven by an and gate.

To model this using a using a with select statement in VHDL, we would need to write code which specifically models the AND gate.

We must then include the output of this code in the with select statement which models the multiplexer.

The code snippet below shows this implementation.

addr <= a and b;
with addr select mux_out <=
  a when '1',
  b when others;  

Although this code would function as needed, using a when else statement would give us more succinct code. Whilst this will have no impact on the way the device works, it is good practice to write clear code. This help to make the design more maintainable for anyone who has to modify it in the future.

The VHDL code snippet below shows the same circuit implemented with a when else statement.

mix_out <= a when (a = '1' and b = '1') else b;

Instantiating Components in VHDL

Up until this point, we have shown how we can use the VHDL language to describe the behavior of circuits.

However, we can also connect a number of previously defined VHDL entity architecture pairs in order to build a more complex circuit.

This is similar to connecting electronic components in a physical circuit.

There are two methods we can use for this in VHDL – component instantiation and direct entity instantiation.

VHDL Component Instantiation

When using component instantiation in VHDL, we must define a component before it is used.

We can either do this before the main code, in the same way we would declare a signal, or in a separate package.

VHDL packages are similar to headers or libraries in other programming languages and we discuss these in a later post.

When writing VHDL, we declare a component using the syntax shown below. The component name and the ports must match the names in the original entity.

component <component_name> is
  port (
    <port_name1> : <mode> <signal_type>
end component <component_name>;

After declaring our component, we can instantiate it within an architecture using the syntax shown below. The <instance_name> must be unique for every instantiation within an architecture.

<instance_name> : component <component_name>
  port map (
    <port_name1> => <signal_name1>,
    <port_name2> => <signal_name>

In VHDL, we use a port map to connect the ports of our component to signals in our architecture.

The signals which we use in our VHDL port map, such as <signal_name1> in the example above, must be declared before they can be used.

As VHDL is a strongly typed language, the signals we use in the port map must also match the type of the port they connect to.

When we write VHDL code, we may also wish to leave some ports unconnected.

For example, we may have a component which models the behaviour of a JK flip flop. However, we only need to use the inverted output in our design meaning. Therefore, we do not want to connect the non-inverted output to a signal in our architecture.

We can use the open keyword to indicate that we don't make a connection to one of the ports.

However, we can only use the open VHDL keyword for outputs.

If we attempt to leave inputs to our components open, our VHDL compiler will raise an error.

VHDL Direct Entity Instantiation

The second instantiation technique is known as direct entity instantiation.

Using this method we can directly connect the entity in a new design without declaring a component first.

The code snippet below shows how we use direct entity instantiation in VHDL.

<instance_name> : entity <library_name>.<component_name>(<architecture_name>)
  port map (
    <port_name1> => <signal_name1>,
    <port_name2> => <signal_name>

As with the component instantiation technique, <instance_name> must be unique for each instantiation in an architecture.

There are two extra requirements for this type of instantiation. We must explicitly state the name of both the library and the architecture which we want to use. This is shown in the example above by the <library_name> and <architecture_name> labels.

Once the component is instantiated within a VHDL architecture, we use a port map to connect signals to the ports. We use the VHDL port map in the same way for both direct entity and component instantiation.


Which types can not be used with the VHDL logical operators?

Scalar types such as integer and real.

Write the code for a 4 input NAND gate

nand_out <= a nand b nand c nand d;

We can use two different types of statement to model multiplexors in VHDL, what are they?

The with select statement and the when else statement

Write the code for an 8 input multiplexor using both types of statement

-- Using the with select statement
with sel select mux_out =>
  a when x"0",
  b when x"1",
  c when x"2",
  d when x"3",
  e when x"4",
  f when x"5",
  g when x"6",
  h when others;
-- Using the when else statement
mux <= a when sel = x"0"
    else b when sel = x"1"
    else c when sel = x"2"
    else d when sel = x"3"
    else e when sel = x"4"
    else f when sel = x"5"
    else g when sel = x"6"
    else h;

Write the code to instantiate a two input AND component using both direct entity and component instantiation. Assume that the AND gate is compiled in the work library and the architecture is named rtl.

-- First of all declare the component
component and2 is
  port (
    a       : in std_logic;
    b       : in std_logic;
    and_out : out std_logic
end component and2;
-- Then instantiate the component
and2_comp_example: component and2
  port map (
    a       => a1,
    b       => b1,
    and_out => and_out1
-- Instantiate the component
and2_entity_example: entity work.and2(rtl)
  port map (
    a       => a2,
    b       => b2,
    and_out => and_out2
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