ECOM 4311—Digital System Design with VHDL

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Chapter 4Dataf low Style Combinational Design

Introduction

• Combinational systems have no memory. A combinational system’s outputs are functions of only its present input values.

• When using VHDL, logic minimization is performed automatically by the synthesizer and place-and-route tools. This results in a significant reduction in design effort.

• VHDL provides a full set of logical operators that can be used on scalar or array objects. Using these operators, we can easily write descriptions for combinational systems.

LOGICAL OPERATORS

• The logical operators, which are predefined in package STANDARD for types bit and boolean, are:

• VHDL not is classified as a miscellaneous operator. Miscellaneous operators have the highest precedence.

• the logical operators have have the same level of precedence and the lowest precedence of all VHDL operators.

• In the absence of parentheses, operators at the same precedence level are associated with their operands in textual order from left to right.

logical_operator ::=and | or | nand | nor | xor | xnor

Order of Evaluation

• Parentheses must be used in an expression to force any other order of evaluation. Expressions within parentheses are evaluated first.

c = a and not b or not a and b

c = ((a and (not b)) or (not a)) and b

c <= (a and not b) or (not a and b);

Nonassociative Logical Operators

f <= a and b and c;

g <= a nand b nand c; -- invalid

g <= not (a and b and c); -- valid

Logical Operations on Array Elements

• The logical operators can be used to operate on elements of arrays by indexing specific elements.

entity and_vector1 isport (x, y : in std_logic_vector(3 downto 0);f : out std_logic_vector(3 downto 0));end and_vector1;architecture dataflow1 of and_vector1 isbeginf(3) <= x(3) and y(3);f(2) <= x(2) and y(2);f(1) <= x(1) and y(1);f(0) <= x(0) and y(0);end dataflow1;

Logical Operations on Entire Arrays

• When dealing with two arrays of the same length and type, the logical operators can be applied to the entire arrays. The result is an array of the same length.

architecture dataflow2 of and_vector1 isbeginf <= x and y;end dataflow2;

Array Element Matching

architecture dataflow1 of and_vector2 isbeginf <= x and y;end dataflow1;

architecture dataflow2 of and_vector2 isbeginf(3) <= x(3) and y(0);f(2) <= x(2) and y(1);f(1) <= x(1) and y(2);f(0) <= x(0) and y(3);end dataflow2

entity and_vector2 isport (x : in std_logic_vector(3 downto 0);y : in std_logic_vector(0 to 3);f : out std_logic_vector(3 downto 0));end and_vector2;

Signal Assignment Statement

• A synthesizable signal assignment statement has the form:

• Three kinds of concurrent signal assignment statements in the dataflow style :Concurrent signal assignment statement using a Boolean

expressionSelected signal assignment statementConditional signal assignment statement

• A concurrent signal assignment statement using a Boolean expression assigns the value of the expression to a signal. For example:

target <= value_expression;

f <= a and b;

A 4-to-1 multiplexer with data inputs treated as a vector

CONDITIONAL SIGNAL ASSIGNMENT

• A conditional signal assignment allows a signal to be assigned a value based on a set of conditions.

• The conditions are expressions involving relational operators.

• Conditional signal assignment statement, also called a when-else statement.

Syntax

• Simplified syntax:

• •

• The boolean_expr_i return true or false and are each evaluated from top-to-bottom until one is found to be true

• When this occurs, the value_expr_i is assigned to the signal_name signal

• The last value_expression must not have an associated when condition.

target <= value_expression_1 when condition1 else value_expression_2 when condition2 else ... value_expression_n-1 when conditionn-1 else value_expression_n;

A 4-bit comparator using multiple conditional signal assignment statements.

A 4-to-1 multiplexer using an aggregate for control and select inputs

E.g., 8-bit 4-to-1 mux

• This is the truth table for an 8-bit, 4-to-1 multiplexer

• Here, a, b, c, and d are input signals each of 8-bits

• s is also an input, i.e., a 2-bit signal the input data to route to the output

E.g., 8-bit 4-to-1 mux

• Some synthesis software allows the following alternative expression

E.g., 2-to-22 binary decoder

• An n-to2n decoder has an n-bit input and a 2n-bit output, where each bit of the output represents an input combination

Function table

E.g., 2-to-22 binary decoder

E.g., 4-to-2 priority encoder

• It checks the input requests and generates the code of the request with highest priority.

• There are four input requests, r(3), ..., r(0)

• The outputs include a 2-bit signal (code), which is the binary code of the highest priority request and a 1-bit signal active that indicates if there is an active request

Function table

E.g., 4-to-2 priority encoder (active low)

output inputa i0 i1 i2 i3

0 0 _ _ _ 01 0 _ _ 0 10 1 - 0 1 11 1 0 1 1 1

Don’t Care Inputs (std_match)

Selected Signal Assignment Statement

• A selected signal assignment statement, also called a with-select-when statement, allows one of several possible values to be assigned to a signal based on a select expression.

• The select expression must be a discrete type or a one-dimensional character array type

Selected Signal Assignment Statement

• Simplified syntax:with select_expression select signal_name <= value_expr_1 when choice_1, value_expr_2 when choice_2, value_expr_3 when choice_3, . . . value_expr_n when choice_n;

Example:with s selectx <= "0001" when "00", "0010" when "01", "0100" when "10", "1000" when others;

• select_expression Discrete type or 1-D arrayWith finite possible values

• choice_iA value of the data type, if bit_vector(1 downto 0) used in

select_expression, then choices must be "00", "01", "10" and "11"

• Choices must bemutually exclusiveall inclusiveothers can be used as last choice_i list of choices can be associated separating each choice using

Important Points Example:with s selectx <= "0001" when "00", "0010" when "01", "0100" when "10", "1000" when others;

Using an aggregate in a select expression Example:

Note: Type Qualification

• We want to use an aggregate

• The compiler does not simply assume that an aggregate of std_logic elements is type std_logic_vector, since there are other array types, such as unsigned, that have std_logic elements.

• We must explicitly specify the aggregate’s type. This is accomplished using a type qualification.

std_logic_vector'(g_bar, b, a)

(g_bar, b, a)

Example: 2 by 4 Decoder

Example: 2 by 4 Decoder (continue….)

E.g., 4-to-2 priority encoder• Recall that "11" is assigned to code if r(3) is ’1’• The shortcut taken in the conditional assignment stmt, i.e., code <= "11"

when (r(3)=’1’) else• Can NOT be taken here and all 8 values that have a ’1’ for r(3) must be

listed, e.g., “1000", "1001", "1010",…….., "1111" • You might be tempted to make this more compact by using the ’-’ (don’t-

care) as

• But this doesn’t work since the ’-’ value never occurs in a real circuit

Don’t Care Outputs

• Assignments of “don’t care” values to outputs are very useful because they allow a synthesizer to take advantage of the “don’t cares” to minimize the logic it synthesizes.

• Consider the design of a system that takes a BCD input and generates a '1' output only when the BCD input is valid and represents a digit greater than 5

Example: BCD digit greater than 5 design that does not use “don’t care” outputs

Example: BCD digit greater than 5 design that uses “don’t care” outputs

Some synthesizers also accept use of the std_logic value 'X' to specify a “don’t care” output

VHDL relational operators

Operand types must be the same. The result of a relational operation is always type boolean.Type boolean is an enumeration type predefined in package STANDARD as:

type boolean is (false, true);

A 3-to-8 decoder description (74Ls138).

Decoder 74138 (continue..)

Description of a BCD to seven-segment decoder.

Description of a BCD to seven-segment decoder (continue….)

TABLE LOOKUP

• A simple way to describe a combinational system is to use a table lookup.

• For a system with a single output the table is represented as a constant vector.

• For a system with multiple outputs an array of constant vectors is used.

• For any input combination we can then determine the output by simply looking it up in the table.

Table lookup for a system with a single output

A 2-bit binary to reflected code conversion described as a table lookup.

A three-state buffer

• A three-state buffer (tristate buffer) has a data input and an enable input.

• Its enable input controls whether the three-state buffer is OFF and its output is high impedance ('Z'), or whether it is ON and its output is driven by its data input.

• Thus, the output of a three-state buffer can be either '0', '1', or 'Z'.

Describing Three-state Output Ports in VHDL

Multiplexing Two Data Sources

Homework#3

• Solve the following problems from the textbook chapter2:

2, 3, 8, 9, 15, 18, 23, 24, 28,33, 35,36

Any Question

Finally!!

ECOM 4311—Digital System Design with VHDL

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