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EENG 2710 Chapter 4

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EENG 2710 Chapter 4

Modular Combinational Logic

Chapter 4 Homework

EENG 2710 Xilinx Project 1

And

EENG 2710 VHDL Project 2

(Projects are on Instructor’s Website)

- Decoder: A digital circuit designed to detect the presence of a particular digital state.
- Can have one output or multiple outputs.
- Example: 2-Input NAND Gate detects the presence of ‘11’ on the inputs to generate a ‘0’ output.

- Uses single gates (AND/NAND) and some Inverters.
- Example: 4-Input AND detects ‘1111’ on the inputs to generate a ‘1’ output.
- Inputs are labeled D3, D2, D1, and D0, with D3 the MSB (most significant bit) and D0 the LSB (least significant bit).

D3

D3

D2

D2

D1

D1

D0

D0

Y = (D3

D2

D1

D0)’

Y = D3

D2

D1

D0

- If the inputs to a 4-Input NAND are given as
, then the NAND detects the code 0001. The output is a 0 when the code 0001 is detected.

- This type of decoder is used in Address Decoding for a PC System Board.

- Decoder circuit with n inputs can activate m = 2n load circuits.
- Called a n-line-to-m-line decoder, such as a 2-to-4 or a 3-to-8 decoder.
- Usually has an active low enable that enables the decoder outputs.

74138 3-to-8 Decoder

- Simulation: The verification of a digital design using a timing diagram before programming the design in a Complex Programmable Logic Device (CPLD).
- Used to check the Output Response of a design to an Input Stimulus using a timing diagram.

- Use select signal assignment statements constructs or conditional signal assignment statements constructs.

- Using a select signal assignment statement:
LIBRARY ieee;

USE ieee.std_logic_1164.ALL;

ENTITY decode3a IS

PORT(

d : IN STD_LOGIC_VECTOR (1 downto 0);

g : IN STD_LOGIC

y : OUT STD_LOGIC_VECTOR (3 downto 0));

END decode3;

- In the previous slide, the Entity used a STD LOGIC Array for Inputs and Outputs.
- The Y : OUT STD_LOGIC_VECTOR(3 downto 0) is equal to Y3, Y2, Y1, Y0.
- The STD_LOGIC Data Type is similar to BIT but has added state values such as Z, X, H, and L instead of just 0 and 1.

- Uses a VHDL Architecture construct called WITH SELECT.
- Format is:
- WITH (signal input(s)) SELECT.
- Signal input states are used to define the output state changes.

ARCHITECTURE decoder OF decode2to4 IS

SIGNAL inputs : STD_LOGIC_VECTOR (2 downto 0);

BEGIN

inputs(2)<= g;

inputs (1 downto 0)<= d;

WITH inputs SELECT

y <= "0001" WHEN "000",

"0010" WHEN "001",

"0100" WHEN "010",

"1000" WHEN "011",

"0000" WHEN others;

END decoder;

d(1)

g

d(0)

Default case

Y(3)

Y(0)

LIBRARY ieee;

USE ieee.std_logic_1164.ALL;

ENTITY decode3a IS

PORT(

d : IN STD_LOGIC_VECTOR (1 downto 0);

g : IN STD_LOGIC

y : OUT STD_LOGIC_VECTOR (3 downto 0));

END decode3;

ARCHITECTURE decoder OF decode2to4 IS

SIGNAL inputs : STD_LOGIC_VECTOR (2 downto 0);

BEGIN

inputs(2)<= g;

inputs (1 downto 0)<= d;

WITH inputs SELECT

y <= "0001" WHEN "000",

"0010" WHEN "001",

"0100" WHEN "010",

"1000" WHEN "011",

"0000" WHEN others;

END decoder;

- The decoder Architecture used a SELECT to evaluate d to determine the Output y.
- Both d and y are defined as an Array (or bus or vector) Data Type.
- The last state for WHEN OTHERS is added for the other logic states (Z, X, H, L, etc.).

- Seven-Segment Display: An array of seven independently controlled LEDs shaped like an 8 that can be used to display decimal digits.

- Common Anode Display (CA): A seven- segment display where the anodes of all the LEDs are connected together to VCC and a ‘0’ turns on a segment (a to g).

- Common Cathode Display (CC): A seven-segment display where all the cathodes are connected and tied to ground, and a ‘1’ turns on a segment.

- Receives a BCD (Binary Coded Decimal) 4-Bit input, outputs a BCD digit 0000 – 1001 (0 through 9).
- Generates Outputs (a–g) for each of the display LEDs.
- Requires a current limit series resistor for each segment.

- Decoders for a CC-SS have active high outputs while decoders for a CA-SS have active low outputs (a to g).
- The outputs generated for the binary input combinations of 1010 to 1111 are “don’t cares”.
- The decoder can be designed with VHDL Logic (7447, 7448).

ENTITY bcd_7seg IS

PORT(

d3, d2, d1, d0: IN BIT;

a, b, c, d, e, f, g: OUT BIT;

END bcd_7seg;

ARCHITECTURE seven_segment OF bcd_7seg IS

SIGNAL input: BIT_VECTOR (3 downto 0);

SIGNAL output: BIT_VECTOR (6 downto 0);

BEGIN

input <= d3 & d2 & d1 & d0;

-- Uses two intermediate signals called input and output (internal no pins)

-- Creates an array by using the concatenate operator (&)

In this case input(3) <= d3, input(2) <= d2, etc.

WITH input SELECT

output <= “0000001” WHEN “0000”,

“1001111” WHEN “0001”,

“0010010” WHEN “0010”,

“0000110“ WHEN “0011”,

• • •

• • •

• • •

“1111111” WHEN others;

a<=output(6);

b<=output(5);

c<=output(4);

d<=output(3);

e<=output(2);

f<=output(1);

g<=output(0);

END seven_segment

- In the preceding example file, a concurrent select signal assignment was used (WITH (signals) SELECT.
- The intermediate output signals were mapped to the segments (a to g).
- Example: when Input (D3 – D0) is 0001, the decoder sets a=d=e=f=g=1, b=c=0.

- Encoder: A digital circuit that generates a specific code at its outputs in response to one or more active inputs.
- It is complementary in function to a decoder.
- Output codes are usually Binary or BCD.

- Priority Encoder: An encoder that generates a code based on the highest- priority input.
- For example, if input D3 = input D5, then the output is 101, not 011. D5 has a higher priority than D3 and the output will respond accordingly.

D9 – D0 = 0100001111

BCD # = ?

D9 – D0 = 0101001011

Q3 – Q0 = 1000 (810)

D9 – D0 = 1000000001

Q3 – Q0 = 1001 (910)

D9 – D0 = 1101001011

Q3 – Q0 = 1001 (910)

D

= 1

C

= 0

B

= 0

A

= 0

1

-- hi_pri8a.vhd

ENTITY hi_pri8a IS

PORT(

d: IN BIT_VECTOR (7 downto 0);

q: OUT BIT_VECTOR (2 downto 0));

END hi_pri8a;

ARCHITECTURE a OF hi_pri8a IS

BEGIN

-- Concurrent Signal Assignments

q(2)<=d(7) or d(6) or d(5) or d(4);

q(1)<=d(7) or d(6)

or ((not d(5)) and (not d(4)) and d(3))

or ((not d(5)) and (not d(4)) and d(2));

q(0)<=-- in a similar fashion

END a;

- (MUX): A digital circuit that directs one of several inputs to a single output based on the state of several select inputs.
- A MUX is called a m-to-1 MUX.
- A MUX with n select inputs will require m = 2n data inputs (e.g., a 4-to-1 MUX requires 2 select inputs S1 and S0).

- Boolean expression for a 4-to-1 MUX is
- This expression can be expanded to any size MUX so the VHDL architecture could use a very long concurrent Boolean statement.

- Naming convention in which variables are bundled in numerically related groups, the elements of which are themselves numbered.
- The first subscript identifies the group that a variable belongs to (D01, D00).
- The second subscript indicates which element of the group a variable represents.

- The following three VHDL constructs can be used to describe the Multiplexer:
- Concurrent Signal Assignment Statement
- Select Signal Assignment Statement
- CASE Statement

PROCESS: A VHDL construct that contains statements that are executed if a signal in its sensitivity list changes.

Sensitivity list: A list of signals in a PROCESS statement that are monitored to determine whether the Process should be executed.

- A case statement is a VHDL construct in which there is a choice of statements to be executed, depending on the value of a signal or variable.

CASE __expression IS

WHEN __constant_value =>

__statement;

__statement;

WHEN __constant_value =>

__statement;

__statement;

WHEN OTHERS =>

__statement;

__statement;

END CASE;

Basic Entity declaration for a 4-to-1 MUX:

ENTITY mux4case IS

PORT(

d0, d1, d2, d3 : IN BIT;

s: IN BIT_VECTOR (1 downto 0);

y: OUT BIT);

END mux4case;

ARCHITECTURE mux4to1 OF mux4case IS

BEGIN

-- Monitor select inputs and execute if they change

PROCESS(s)

BEGIN

CASE s IS

WHEN "00"=>y<=d0;

WHEN "01"=>y<=d1;

WHEN "10"=>y<=d2;

WHEN "11"=>y<=d3;

WHEN others=>y<='0';

END CASE;

END PROCESS;

END mux4to1;

- Used in directing multiple data sources to a single processing element such as multiple CD Player Streams to a DSP.
- Used in Time Division Multiplexing (TDM) by the Phone Service to multiplex multiple voice channels on a single coax line (or fiber).

Multiplexer Applications

Used in directing multiple data sources to a single processing element such as multiple CD Player Streams to a DSP.

Multiplexer Applications

Used in Time Division Multiplexing (TDM) by the Phone Service to multiplex multiple voice channels on a single coax line (or fiber).

- Each user has a specific time slot in a TDM data frame. Each frame has 24 users.
- TDM requires a time-dependent (counter) source to synchronize the select lines.
- Each user’s time slot repeats on the next frame for more data.
- The links are called T-Carriers (such as a T1 Line).

- Two methods in which data is transmitted:
- Bit Multiplexing: One bit is sent at a time from the channel during the channel’s assigned time slot
- Word Multiplexing: One byte is sent at a time from the channel during the channel’s assigned time slot

- Demultiplexer: A digital circuit that uses a decoder to direct a single input (from a MUX) to one of several outputs.
- A DEMUX performs the reverse operation of a MUX.
- The selected output is chosen by the Select Inputs (as in a MUX).

- Designated as a 1-to-n DEMUX that requires m select inputs such that n outputs = 2m select inputs.
- 1-to-4 DEMUX Equations:
- They are similar to a MUX and can be designed using CASE Statements.

ENTITY dmux8 IS

PORT(

s: IN STD_LOGIC_VECTOR (2 downto 0);

d: IN STD_LOGIC;

y: OUTSTD_LOGIC_VECTOR (0 to 7));

END dmux8;

ARCHITECTURE a OF dmux8 IS

SIGNAL inputs : STD_LOGIC_VECTOR (3 downto 0);

BEGIN

inputs <= d & s;

WITH inputs select

Y <= “01111111” WHEN “0000”,

“10111111” WHEN “0001”,

• • •

• • •

“11111111” WHEN others;

END a;

- Uses a CMOS Switch or Transmission Gate that will allow a signal to Pass in two directions for + and – Voltages.
- Some commercial types such as a CD4066 or 74HC4066.
- Multiplexes 4 CMOS Switches to a single output (Y) for analog multiplexing.

- Magnitude Comparator: A digital circuit that compares two n-Bit Binary Numbers and indicates if they are equal or which is greater.
- A very simple One-Bit Magnitude Comparator is the Two-Input XNOR Gate:
- When both inputs are equal, the output is a 1; if they are not, it is a 0.

A1

B1

AEQB

A0

B0

A1

B1

AEQB

A0

B0

AGTB

ALTB

- Multiple Bit Comparisons
- Also adds A > B (AGTB) and A < B (ALTB) Outputs.
- For A > B, start with the MSB:
- If An–1 > Bn–1, then AGTB = 1

- If not, then try the next most significant bit.

A3

B3

ALTB

A2

B2

AEQB

A1

B1

A0

AGTB

B0

ENTITY compare4 IS

PORT(

a, b : IN INTEGER RANGE 0 to 15;

agtb, aeqb, altb : OUT STD_LOGIC);

END compare4;

ARCHITECTURE a OF compare4 IS

SIGNAL compare :STD_LOGIC_VECTOR (2 downto 0);

BEGIN

PROCESS (a, b)

BEGIN

IF a<b THEN

compare <= “110”;

ELSIF a = b THEN

compare <= “101”;

ELSIF a > b THEN

compare <= “011”;

ELSE

compare <= “111”;

END IF;

agtb <= compare(2);

aeqb <= compare(1);

altb <= compare(0);

END PROCESS

END a;

- Parity: A digital system that checks for errors in a n-Bit Binary Number or Code.
- Even Parity: A parity system that requires the binary number and the parity bit to have an even # of 1s.
- Odd Parity: A parity system that requires the binary number and the parity bit to have an Odd # of 1s.

- Parity Bit: A bit appended on the end of a binary number or code to make the # of 1s odd or even depending on the type of parity in the system.
- Parity is used in transmitting and receiving data by devices in a PC called UARTs, that are on the COM Port.
- UART = Universal asynchronous
Receiver/Transmitter

- N1 = 0110110:
- It has four 1s (an even number).
- If Parity is ODD, the Parity Bit = 1 to make it an odd number (5).
- If Parity is EVEN, the Parity Bit = 0 to keep it an even number (4).

- N2 = 1000000:
- One 1 in the data.
- Podd = 0.
- Peven = 1.

- A basic two-bit parity generator can be constructed from a XOR Gate.
- When the two inputs are 01 or 10, the output is a 1 (so this is even parity).
- When the two inputs are 00 or 11, the output is a 0.
- For a parity generator of n bits, add more gates.

- Cascading a long chain of XOR gates could cause excessive propagation delays.
- To check for a Parity error, the receiver (RX) just generates a new Parity Bit (P1) based on the received parallel data and then compares it to the parity bit transmitted (P2).

- If there is an error, the two bits (P1 and P2) will not be equal, and we can use a two-bit magnitude comparator to check this (an XOR gate).
- This check is called syndrome.
- If there are no errors, the syndrome output (Perr) is 0.

- Parity is not a foolproof system.
- If two bits are in error, the error is not detected.

__generate_label:

FOR __index_variable IN __range GENERATE

__statement;

__statement;

END GENERATE;

LIBRARY ieee;

USE ieee.std_logic1164.ALL;

ENTITY parity4_gen IS

PORT(

d : IN STD_LOGIC_VECTOR (0 to 3);

pe ; OUT STD_LOGIC);

END parity4_gen;

ARCHITECTURE parity OF parity4_gen IS

SIGNAL p : STD_LOGIC_VECTOR (1 to 3);

BEGIN

p(1) <= d(0) xor d(1);

parity_generate:

FOR i IN 2 to 3 GENERATE

p(i) <= p(i-1) xor d(i);

END GENERATE;

pe <= p(3);

END parity;

- Half Adder (HA): A circuit that will add two bits and produce a sum bit and a carry bit.
- Full Adder (FA): A circuit that will add a carry bit from another HA or FA and two operand bits to produce a sum bit and a carry bit.

- Binary Two-Bit Addition Rules:
0 + 0 = 00

0 + 1 = 01

1 + 1 = 10

- Basic Equations: S = A XOR B, C = A and B where S = Sum and C = Carry.
- Truth Table for HA Block:

- Adds a CIN input to the HA block.
- Equations are modified as follows:
- A FA can be made from two HA blocks and an OR Gate.

- A circuit, consisting of n full adders, that will add n-bit binary numbers.
- The output consists of n sum bits and a carry bit.
- COUT of one full adder is connected to CIN of the next full adder.

- In the n-Bit Parallel Adder (FA Stages) the Carryout is generated by the last stage (FAN).
- This is called a Ripple Carry Adder because the final carryout (Last Stage) is based on a ripple through each stage by CIN at the LSB Stage.

- Each Stage will have a propagation delay on the CIN to COUT of one AND Gate and one OR Gate.
- A 4-Bit Ripple Carry Adder will then have a propagation delay on the final COUT of 4 2 = 8 Gates.
- A 32-Bit adder such as in an MPU in a PC could have a delay of 64 Gates.

- Fast Carry or Look-Ahead Carry:
- A combinational network that generates the final COUT directly from the operand bits (A1 to An, B1 to Bn).
- It is independent of the operations of each FA Stage (as the ripple carry is).

- Fast Carry has a small propagation delay compared to the ripple carry.
- The fast carry delay is 3 Gates for a 4-Bit Adder compared to 8 for the Ripple Carry.

- The concept of Subtraction using 2’s Complement addition allows a Parallel FA to be used.
- The subtract operation involves adding the inverse of the subtrahend to the minuend and then adding a 1.

- This operation can be done in a parallel n-Bit FA by inverting (B1 to Bn) and connecting CIN at the LSB Stage to +5 V.
- The circuit can be modified to allow either the ADD or SUBTRACT operation to be performed.

- XOR gates are used as programmable inverters to pass binary numbers (e.g., B1B2B3B4) to the parallel adder in true or complemented form.

1

X

B

B’

B

B

Y

B

X=1

X=0

0

- If the sign bits of both operands are the same and the sign bit of the sum is different from the operand sign bits, an overflow has occurred.
- Overflow is not possible if the sign bits of the operands are different from each other.

- Adding two 8-bit negative numbers:
- Adding two 8-bit positive numbers:

- A Parallel Adder whose output sum is in groups of 4 bits, each representing a BCD (8421) Digit.
- Basic design is a 4-Bit Binary Parallel Adder to generate a 4-Bit Sum of A + B.
- Sum is input to the four-bit input of a Binary-to-BCD Code Converter.