Instructor: Yuzhuang Huyhu1@cs.sfu.ca

Course TimetableLectures: Wednesday 17:30-20:20, HCC 2510

Labs: Thursday 17:30-18:20, HCC 7050

Midterm, Final: TBA

Office Hours: Instructor: Friday 14:30-16:30, HCC 2134 TA: TBA

Contact InformationInstructor: Yuzhuang Hu Email: yhu1@cs.sfu.ca Office Hours: Friday 2:30pm-4:30pm Office: HC 2134 Phone: 778-782-8740

TA: Zhiyong Lu Email: zhiyong@cs.sfu.ca Office Hours: TBA

Marking Scheme

4 Assignments + Labs, 30% Late Penalty: -20% per day

Midterm, 20%

Final, 50%

What is Computer Architecture?Instruction Set Architecture: the actual

programmer visible instruction set.

Implementation Organization: high level aspects of a

computer’s design. Hardware: specifics of a machine, e.g., the

detailed logic design.

A Personal ComputerScreen

Keyboard

Hard drive

Drive Controll

er

Bus Interface

RAMProcesso

r

Graphics

Adapter

CPU, FPU, MMUInternal Cache

External Cache

Von Neumann ArchitectureMemory

Input/Output

Control Unit

Data PathCPU

• Stored program concept.

Binary Numbers

Digital signals are in fact analog. 0 and 1 are represented by voltage ranges.

0.5

0.0

1.0

Time

Voltage(Volts)

0

1

Time

Number Systems

Decimal numbers are of base 10, e.g., 724 = 7 ×102 + 2×101 + 4×100

Binay numbers are of base 2, e.g., (1101)2 = 1×23 + 1×22 + 0×21 + 1×20 = 13

Convert a decimal number N to binaryLoop remainder = N mod 2 add remainder to the left of the result N = N / 2An example:

14

7

3

1

22

2

0 result

10

110

1110

0remainder

1

1

1

Full Adder

A full adder considers a carry in bit.

Truth Table of Full Adder

Inputs

X Y Z C S

Outputs

0 0 0 0 00 10 11 0

0 0 10 1 00 1 11 0 01 0 11 1 01 1 1

0 11 01 01 1

Binary SubtractionMethod 1: First compare the subtrahend with the minuend.

Then subtract the smaller from the larger.

Method 2: Directly subtract the subtrahend from the minuend. An example:

Borrows into:Minuend:

1100010011

-11110Subtrahend:

10101Difference:-01011Correct

Difference:

Complements2’s complement of a binary number M is

defined to be the number 2n – M .

1’s complement of a binary number M is defined to be the number (2n – 1) – M .

1’s complement of M can be obtained by subtracting 1 each digit from 1. 2’s complement of M = 1’s complement of M + 1.

Subtraction Using 2s Complement• Task: compute M – N, where M and N are two n-

digit unsigned numbers.

Add the 2s complement of N to M. This performs M + (2n – N) = M – N + 2n.

If M ≥ N, discard the end carry, leaving M – N.

If M < N, the sum equals 2n – (N – M). Do a correction by taking the 2s complement of the sum and place a minus sign in front.

Signed Numbers• A binary number M can be represented by:

Signed-magnitude system: Add 0 to the left of M if M ≥ 0, and add 1 to the left of M if M < 0. For example, +7 = 0111, -7 = 1111.

Signed-complement system: Add 0 to the left of M if M ≥ 0, and add 1 to the left of the 2s complement of M if M < 0. For example, +7 = 0111, -7 = 1001.

Signed Binary Addition and Subtraction• The subtraction of M – N under the signed-

magnitude representation: similar to the unsigned subtraction using 2’s complements.

• The subtraction of M – N under the complement representation : obtained from the addition of the two numbers, including their sign bits. A carry out of the sign bit position is discarded. No comparison or subtraction is needed.

Signed Binary Subtraction contd.When M is positive, and N is negative: This

performs M + 2n + (2n – N)=M – N + 2n+1. If M - N ≥ 0, then the sign bit is 0 after discarding the carry. If M - N < 0, there is no carry out and the sign bit is 1.

It can be similarly argued when M is negative, and N is positive.

11111010

00001101

00000111

-6

+7

+13

00000110

11010011

11111001

+6

-7

-13

Pitfalls: Overflow!Overflow occurs when the sum takes more

than n+1 bits. Two examples:

An overflow condition can be detected by observing the carry into the sign bit position and the carry out of the sign bit position.

0 1000110

0 1010000

1 0010110

+70

+150

+83

1 0111010

1 0110000

0 1101010

-70

-150

-80

Overflow Detection LogicAn overflow occurs if the above mentioned

two carries are not equal.

N-bit Adder/Subtractor

Cn-1

CnC

V

A Hardware Description Language: VHDL• A hardware description language (HDL) is any

computer language for formal description of digital logic and electronic circuits.

• HDL represents extensive parallel operations, whereas most programming languages represent serial operations.

• VHDL stands for VHSIC Hardware Description Language (Very-High-Speed Integrated Circuits).

Entity Declarations in VHDLentity full_addr is

port ( c_in : in std_logic; x : in std_logic; y : in std_logic; c_out : out std_logic; sum : out std_logic );

end full_addr;

Describing Behaviour in VHDLarchitecture behav of full_addr is

begin

-- Your VHDL code defining the modelc_out <= (x and y) or (x and c_in) or (y and c_in) after 2 ns;

Sum <= x xor y xor c_in after 2 ns;

end behav;

Full Adder

xy

c_in c_outsum

Truth Table of Full Adder

InputsX Y Z C S

Outputs

0 0 0 0 00 10 11 0

0 0 10 1 00 1 11 0 01 0 11 1 01 1 1

0 11 01 01 1

Describing Structure in VHDL architecture structure of full_addr is signal s1, s2, s3:std_logic; Begin G1:xor_3 port map(INA=>c_in, INB=>x, INC=>y, Y=>sum); G2:and_2 port map(INA=>c_in,INB=>x, Y=>s1); G3:and_2 port map(INA=>x,INB=>y, Y=>s2); G4:and_2 port map(INA=>c_in,INB=>y, Y=>s3); G5:or_3 port map(INA=>s1,INB=>s2, INC=>s3,Y=>c_out); end structure;

Signals in VHDLSignals are used in VHDL to interconnect

components.

Signals have propagation delays. They behave like some real wires.

Each signal can have only one source.

Discrete Event Time ModelWe need to simulate VHDL programs to

verify whether the models we built are correct.

In a circuit digital signals change their values concurrently. VHDL simulates the passage of time of the signals in discrete events.

Concurrent Statements in VHDL• Concurrent-Signal-Assignment Statements: sum <= x xor y xor c_in after 2 ns;

• Process-Statements: SUMPROC: process ( x, y, c_in) begin sum <= x xor y xor c_in after 2 ns; end process SUMPROC;

Concurrent Statements Contd.Component-Initiation-Statements: G1:xor_3 port map(INA=>c_in, INB=>x, INC=>y, y=>sum);

An xor gate with 3 inputs would be instantiated, and its inputs would be wired with x, y, and c_in.

Signal Transactions and EventsWhen a signal assignment occurs, VHDL will

treat it as a transaction and schedule the real assignment in some later time.

An event of a signal happens when the signal changes its value.

t1 t3t2 t4 t5

0 ns 0 ns 2 ns 2 ns 4 ns

Some Examples of Generating TransactionsThe current time is 5ns, after executing S <= ‘0’ after 10ns; The transaction list

would be:

The current time is 16ns, after executing S <= ‘1’, ‘0’ after 10ns; The transaction

list would be:

015 ns

116 ns 26 ns

0

Initialization PhaseAll signals are given initialization values.

The simulation time is set to 0.

All processes are executed until they suspend. When executing each signal assignment statement, a transaction on that signal will be generated .

A Simulation Cycle• First Stage: the transactions with the earliest

time will be removed from the list and executed. The simulation time will be forwarded to that time.

• Second Stage: when an event occurs in the first stage, all processes sensitive to the corresponding signal are executed. This means new transactions may be inserted to the list.

Test Bench• A test bench is a VHDL program designed to test your entities. The

entities will be instantiated in the test bench. An example:

entity tb_fa is end tb_fa;

architecture behav of tb_fa is signal x1, y1, c_in1, c_out1 :std_logic; begin x1 <= ‘0’; y1 <= ‘1’; c_in1 <= ‘0’;

UUT: full_addr port map(x=>x1, y=>y1, c_in=>c_in1, c_out=>cout1); end behav;

Variables in VHDL• The simulation cycles do not apply to variables in

VHDL. As in any other programming language, the change on a variable after executing a statement is immediately effective.

• In contrast, assignments on signals are not immediately visible for later sequential statements. A pitfall:

s1 <= ‘0’; ………….. if s1=‘0’ then …………..

It won’t give the answer you want.

THANKS!