digital techniques instructor: dr. andré deutz office: room 116 office phone: 071 - 527 – 7071...

Digital Techniques

Instructor: Dr. André Deutz

Office: Room 116

Office Phone: 071 - 527 – 7071

Email Address: [email protected]

Office Hours: Mondays 16:30-18:00

2

Digital Techniques Lab Assistants Gerben van der Lubbe (email:

[email protected] ) Drs. Dmitry Nadezhkin (email: [email protected];

phone: 071-527-5775) Sjoerd Henstra (email: [email protected]), BSc in

Computer Science Simon Zaaijer (email: [email protected] )

Fall 2007 Digital Techniques by André Deutz, Leiden University

3

Digital Techniques

Text Book:

M.Morris Mano and Charles R. Kime, Logic and Computer Design Fundamentals, 4th Ed., 2008, Pearson Education ; isbn-13: 978-0-13-198926-9; isbn-10: 0-13-198926-X

Useful Link:

The URL of the Companion Website: http://www.prenhall.com/mano

Tip: see also the errata


4

Digital Techniques

References

Snyder, L., Fluency with Information Technology, second edition, 2005, Addison-Wesley (third edition due in October of 2007) (NB this textbook is not required!)

The site of Great Principles of Computing: http://cs.gmu.edu/cne/pjd/GP/


Digital Techniques

Fall 2007 Digital Techniques by André Deutz, Leiden University 5

Lecture Date Topic Reading Assignments

1 Sep 10 Org; computer science; number systems; Chapter 12 Sep 17 Number systems; digital systems & information Chapter 13 Sep 24 Combinational logic circuits Chapter 24 Oct 1 Combinational logic design Chapter 35 Wed 10 Oct

15.00 – 16.45

Physical implementation Part of Chapter 6

6 Oct 15 Arithmetic functions and circuits Part of Chapter 4Oct 22 test

7 Oct 29 Sequential circuits; flip-flops and latches Part of Chapter 58 Nov 5 Sequential circuits; flip-flops and latches; registers Part of Chapter 59 Nov 12 Counters; memory Part of Chapter 5;

Part of Chapter 810 Nov 19 Memory Part of Chapter 811 Nov 26 Processor design Chapter 9 & 1012 Dec 3 Processor design Chapter 9 & 1013 Dec 10 Processor design Chapter 9 & 10

Exam (tentamen): Test, Monday, 22 October; Friday, Jan. 11, 2008; retake 1, Wednesday, Mar. 26, 2008; retake 2, Friday, Aug. 8, 2008

Tentative Course Outline

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Digital Techniques

Test: 14:00 – 17:00; Monday, October 22, 2007

Exam: 14:00-17:00; Friday, Jan. 11, 2008;

retake 1: 14:00-17:00; Wednesday, Mar. 26, 2008;

retake 2: 10:00-13:00; Friday, Aug. 8, 2008

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Digital Techniques

Assignments

There are two kinds of assignments: 1) pencil-and-paper assignments and 2) processor-project assignments.

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Digital Techniques

Collaboration

The pencil-and-paper assignments are done individually. You may work on the processor-project assignments in teams of two. You may consult any source for design and implementation ideas, as long as the synthesis and implementation of these ideas is your own work. It goes without saying that you need to credit any source you are using in your work. The above remarks pertain to both kinds of assignments. If in doubt on how to proceed in this matter, consult the instructor of the course.

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Digital Techniques

DeadlinesPlease submit the assignments by the stated deadlines.

Pencil-and-paper are due 7 days after availability on the web or by email . Therefore you are obliged to check your email and/or web daily (as already stated above). The deadlines for the processor-project assignments will be stated separately. Deadlines are hard deadlines because the answers to the assignments will be posted on the web shortly after the deadline. It goes without saying that we will deal appropriately with exceptionally harsh circumstances beyond your control.

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Digital Techniques

Grade

The grade for the course will be determined by considering the grade for the exam (tentamen), the assignments, and the practicum project. The weights for computing the course grade are as follows:

Exam and Test: 50%

Pencil-and-Paper Assignments: 10%

Processor-Project Assignments : 40%

Moreover the grade for the Exam as well as the grade for the Processor-Project Assignment should exceed 6..

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Digital Techniques

Give a definition of the term Computer Science (informatica).

12

Digital TechniquesGive a definition of the term Computer Science (informatica).Possible answers:To make the digital world (faster), more efficient, and above all more intelligent. The study of phenomena with respect to (digital) computers.The study of representation, analysis, transformation of informationvan Dale: leer van de mechanische verzameling en verwerking van

informatie Van Dale (paar jaar geleden): leer van het verzamelen en de verwerking

van gegevens m.b.v. computers

Computing is the study of information processes, natural and artificial.

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Digital Techniques

Goal of the Course:Our goal is to gain more insight into natural and man-

made/artificial information processes with a focus on man-made/artificial information processing. This goal is, of course, too ambitious and encompasses more than one (if not all) course(s) of our BSc in Computer Science program. A slightly more modest (and perhaps more feasible) goal is to learn to understand information processing à la von Neumann.

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Digital Techniques

Objective

Build a simple computer based on the von Neumann model of computation (which in the man-made world is still the ubiquitous model of computation).

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Digital TechniquesDescriptionIn this course we will learn how to build a simple computer

based on the von Neumann model of computation. To that end we need to study the following topics: Digital

Systems and Information, Number Systems, Binary Arithmetic Operations, Decimal and Alphanumeric Codes, Boolean Algebra, Combinational Logic Circuits, Logic Functions and Circuits, Arithmetic Functions and Circuits, Sequential Circuits, Memory Basics, Registers and Register Transfers, Computer Design Basics.

As simulation tool we will use Digital Works 3.04.The key for Digital Works: 8290-0018-0300-0087

Number Systems

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Overview

Number Systems Positional Number Systems (decimal, binary, octal, and hexadecimal) Number Conversions (r-to-decimal, decimal-to-r, other conversions)

Representations of Numbers in Digital Computers Integer Numbers (unsigned and signed representations)

Arithmetic Operations General Remarks Unsigned, Signed,

Decimal Codes BCD code, Alphanumeric Codes ASCII and Unicode


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Digital Systems: General Remarks

A Digital System manipulates discrete elements/quantities of information

Discrete quantities of information emerge from: the nature of the data being processed the data may be purposely quantized from continues values

Early computer systems were used mostly for numeric computations: the discrete elements used were the digits, hence the term digital computer/system emerged.

In general, any system uses an alphabet (set of symbols) to represent information

The English language system uses an alphabet of 26 symbols (letters) The decimal number system uses an alphabet of 10 symbols (digits)

What about the alphabet of the Digital Systems? Fall 2007 Digital Techniques by André Deutz, Leiden University

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The Digital Systems’ Alphabet is Binary

Digital Systems use only one alphabet with two symbols (digits) ‘0’ and ‘1’ (hence binary ).

A binary digit is called a bit Information is represented by groups of bits

Why is a binary alphabet used? Digital systems have a basic building block called a switch, that can

only be “on” or “off”, i.e., two discrete values ‘0’ and ‘1’ can be distinguished.

An electric device, called a transistor, physically implements the switch.

The two discrete values are physically represented by ranges of voltage values called HIGH and LOW.

“on” (closed) switch corresponds to bit value ‘0’ and is represented by LOW voltage value (between 0.0 and 1.0 Volt).

“off” (open) switch corresponds to bit value ‘1’ and is represented by HIGH voltage value (between 4.0 and 5.0 Volts).

More information will be given later in another lecture.


20

Information Representation

All information in Digital Systems is represented in binary form.

An Aside:Wine merchants in England (13th century or earlier)

2 gills = 1 chopin2 chopins = 1 pint2 pints = 1 quart2 quarts = 1 pottle2 pottles = 1 peck2 pecks = 1 demibushel2 demibushels = 1 bushel or firkin2 firkins = 1 kilderkins2 kilderkins = 1 barrel2 barrels = 1 hogshead2 hogshead = 1 pipe2 pipes = 1 tun


21

Information Representation

All information that is not binary is converted to binary before processed by a Digital Systems.

Decimal numbers are expressed in the binary number system or by means of a binary code.

How is this done? That is not too difficult, once we understand how all

number systems, not only the decimal one (0-9), have a similar formal representation and how a number in one number system can be converted into another.

Let us look into number systems and conversions.


22

Number Systems

Positional number systems The meaning of each digit depends on its position in the number. Example:

Decimal number system (we know it very well and use it in everyday arithmetic).

585.5 is a decimal number in positional code – “5 hundreds plus 8 tens plus 5 units plus 5 tenths”. The hundreds, tens, units, and tenths are powers of 10 implied by the position of the digits.

Decimal number system is said to be of base or radix 10 because it uses 10 distinct digits (0 – 9) and the digits are multiplied by power of 10:

585.5 = 5x102 + 8x101 + 5x100 + 5x10-1

Non-positional number systems Old Roman numbers: for example, XIX equals to 19

Number Systems are employed in arithmetic to represent numbers by strings of digits. There are two types of number systems:


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Positional Number Systems

Number in positional code (An-1An-2…A1A0.A-1A-2…A-m+1A-m)r

r is the base (radix) of the system, r {2, 3, …, I}.

every digit Ai {0, 1, 2, …, r-1}, where {0, 1, 2, …, r-1} is the digit set.

“.” is called the radix point. An-1 is referred to as the most significant digit.

A-m is referred to as the least significant digit.

Number in base r expressed as power series of r An-1 r

n-1 + An-2 r n-2 +…+ A1 r

1 + A0 r 0 + A-1 r

-1 + A-2 r -2 +…+ A-m+1 r

–m+1 + A-m r -m

Example: a number in number systems with base 5 (132.4)5 = 1x52 + 3x51 + 2x50 + 4x5-1 = 25 + 15 + 2 + 0.8 = (42.8)10

We can represent numbers in any number system with base r


24

Binary Number System

Number in positional code (bn-1bn-2…b1b0.b-1b-2…b-m+1b-m)r

r = 2 is the base of the binary system. every digit bi {0, 1}

the digits bi in a binary number are called bits

bn-1 is referred to as the most significant bit (MSB).

b-m is referred to as the least significant bit (LSB).

Number in base 2 expressed as power series of 2 bn-1 2

n-1 + bn-2 2 n-2 +…+ b1 2

1 + b0 2 0 + b-1 2

-1 + b-2 2 -2 +…+ b-m+1 2

–m+1+ b-m 2 -m

Example: a number in the binary number system (1011.01)2 = 1x23 + 0x22 + 1x21 + 1x20 + 0x2-1 + 1x2-2 = 8 + 2 + 1 + 0.25 =

(11.25)10

This is the system used for arithmetic in all digital computers


25

Memorize this table by heart!!!!!!!!

n 2n

n 2n

n 2n

0 1 5 32 10 1024

1 2 6 64 11 2048

2 4 7 128 12 4096

3 8 8 256 13 8192

4 16 9 512 14 16384

Power of Two

024,1210 202 302is 1K (kilo)

is 1M (mega)

is 1G (giga)


26

Other Useful Number System

Octal number system (on-1on-2…o1o0.o-1o-2…o-m+1o-m)8

every digit oi {0, 1, 2, 3, 4, 5, 6, 7}.

on-1 8 n-1 + on-2 8

n-2 +…+ o1 8 1 + o0 8

0 + o-1 8 -1 + o-2 8

-2 +…+ o-m+1 8 –m+1 +o-m 8

-m

(127.4)8 = 1x82 + 2x81 + 7x80 + 4x8-1 = (87.5)10 = (001 010 111.100)2

Hexadecimal number system (hn-1hn-2…h1h0.h-1h-2…h-m+1h-m)16

every digit hi {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F}.

hn-1 16 n-1 + hn-2 16

n-2 +…+ h1 16 1 + h0 16

0 + h-1 16 -1 + h-2 16

-2 +…+ h-m+1 16 –m+1 + h-m

16 –m

(B6F.4)16 = 11x162 + 6x161 + 15x160 + 4x16-1 = (2927.25)10 = (1011 0110

1111.0100)2

Apart from the ordinary binary number system, the octal (base-8) and the hexadecimal (base-16) number systems are useful for representing binary quantities indirectly because their bases are powers of two. These systems have a more compact representation of binary quantities.


27

Another Important Table

Decimal (base 10)

Binary (base 2) Octal (base 8) Hex (base 16)

0 0000 00 0

1 0001 01 1

2 0010 02 2

3 0011 03 3

4 0100 04 4

5 0101 05 5

6 0110 06 6

7 0111 07 7

8 1000 10 8

9 1001 11 9

10 1010 12 A

11 1011 13 B

12 1100 14 C

13 1101 15 D

14 1110 16 E

15 1111 17 FFall 2007 Digital Techniques by André Deutz, Leiden University

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Conversion from base r to DecimalThe conversion of a number in base r to decimal number (base 10) is done by expanding the number in power series and adding all the terms as shown below:

(An-1An-2…A1A0.A-1A-2…A-m+1A-m)r =

An-1 r n-1 + An-2 r

n-2 +…+ A1 r 1 + A0 r

0 + A-1 r -1 + A-2 r

-2 +…+ A-m+1 r –m+1 + A-m r

-m

Example of converting Binary (base 2) to Decimal (base 10):(1011.01)2 = 1x23 + 0x22 + 1x21 + 1x20 + 0x2-1 + 1x2-2 = 8 + 2 + 1 + 0.25 = (11.25)10

Example of converting number in base 5 to Decimal (base 10):(132.4)5 = 1x52 + 3x51 + 2x50 + 4x5-1 = 25 + 15 + 2 + 0.8 = (42.8)10

Example of converting Octal (base 8) to Decimal (base 10):

(127.4)8 = 1x82 + 2x81 + 7x80 + 4x8-1 = (87.5)10

Example of converting Hexadecimal (base 16) to Decimal (base 10):

(B6F.4)16 = 11x162 + 6x161 + 15x160 + 4x16-1 = (2927.25)10


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Conversion from Decimal to base r The conversion is done as follows:1) If the number has a radix point then separate the number into an integer

part and a fraction part, since the two parts must be converted differently.2) The conversion of a decimal integer part to a number in base r is done

by dividing the integer part and all successive quotients by r and accumulating the remainders.

3) The conversion of a decimal fraction part to a number in base r is done by multiplying the fractional parts by r and accumulating integers.

Example of converting Decimal (base 10) to Binary (base 2): (41.6875)10

Converting the integer part (41)10 :

41/2 = 20 + 1/2 Remainder = 1 LSB

20/2 = 10 + 0/2 010/2 = 5 + 0/2 0 5/2 = 2 + 1/2 1 2/2 = 1 + 0/2 0 1/2 = 0 + 1/2 1 MSB

(41)10 = (101001)2

Converting the fraction part (0.6875)10 :

0.6875 x 2 = 1.3750 Integer = 1 MSB

0.3750 x 2 = 0.7500 00.7500 x 2 = 1.5000 10.5000 x 2 = 1.0000 1 LSB

(0.6875)10 = (0.1011)2

(41.6875)10 = (101001.1011)2


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Other Conversions

Binary to Octal or Hexadecimal: grouping bits starting from the radix point (1101010.01)2 to Octal (groups of 3): (001|101|010.010|)2 = (152.2)8

(1101010.01)2 to Hex (groups of 4): (0110|1010.0100|)2 = (6A.4)16

Octal to Binary: convert each digit to binary using 3 bits (475.2)8 = (100 111 101. 010)2

Hexadecimal to Binary: convert each digit to binary using 4 bits (7A5F.C)16 = (0111 1010 0101 1111. 1100)2 = (111101001011111.11)2

Hexadecimal to Octal Hexadecimal Binary Octal

Octal to Hexadecimal Octal Binary Hexadecimal


31

Number Ranges

The range of numbers in base (radix) r depends on the number of digits used to represent the numbers.

Assume the number (An-1An-2…A1A0.A-1A-2…A-m+1A-m)r represented by n digits for the integer part and m digits for the fraction part.

The smallest integer number is 0 and the largest is (r-1) r n-1 + (r-1) r

n-2 + …+ (r-1)r

1 + (r-1) r 0 = rn-1 ,i.e., the range is from 0 to rn-1

The smallest fraction number is 0.0 and the largest is (r-1) r -1 + (r-1) r

-2 + …+ (r-1) r

–m+1 + (r-1) r –m = 1- r

–m ,i.e., the range is from 0.0 to 1- r –m

The range of numbers is from 0.0 to rn - r –m

Examples: Largest 3-digit integer decimal (base 10) number is 103-1 = 1000 - 1 = 999 Largest 8-digit integer binary (base 2) number is (11111111)2 ,i.e., 28-1 = 255 Largest 5-digit decimal (base 10) fraction is 1-10-5 = 1 – 0.00001 = 0.99999 Largest 16-digit binary (base 2) fraction is 1-2-16 = 0.9999847412

What about the range of negative numbers?Fall 2007 Digital Techniques by André Deutz, Leiden University

32

Representations of Numbers in Digital Computers (1)

Numbers are represented in binary format as strings of bits Bit is the smallest binary quantity with a value of 0 or 1. Byte is a string (sequence) of eight bits. Word is a string (sequence) of n bits (n > 8). In most cases n is a

power of 2 (n = 24 = 16, n = 25 = 32, n = 26 = 64, etc…). Examples bit: 1 byte: 01101111 16-bit word: 11110100 10001010

Positive Integer Numbers Positive integers and the number zero can be represented as

unsigned binary numbers using a byte or an n-bit word. Magnitude representation – number N in binary having n bits.

Example: 00001001 ( represents integer number 9 using 8 bits ). Radix complement ( r’s complement ) representation in our case 2’s

complement – Given number N in binary having n bits, the 2’s complement of N is defined as 2n – N .

Example: 11110111 ( 2’s complement of integer number 9 ). Diminished radix complement ( (r-1)’s complement ) representation in

our case 1’s complement - Given number N in binary having n bits, the 1’s complement of N is defined as (2n – 1) – N .

Example: 11110110 ( 1’s complement of integer number 9 ).


33

Representations of Numbers in Digital Computers (2)

Positive and Negative Integer Numbers Positive and negative integers and the number zero can be

represented as signed binary numbers using a byte or an n-bit word where the most significant bit is interpreted as a sign bit. The convention is to make the sign bit 0 for positive numbers and 1 for negative numbers.

Signed-Magnitude representation Example: 0|0001001 ( represents integer number +9 using 8 bits ). Example: 1|0001001 ( represents integer number -9 using 8 bits ).

Signed-Radix complement ( signed-r’s complement ) representation in our case signed-2’s complement (n=8 in the example below)

Example: 0|0001001 ( signed-2’s complement of integer number +9 ). Example: 1|1110111 ( signed-2’s complement of integer number -9 ).

How do we get the signed complement?


34

Arithmetic Operations

Arithmetic operations with numbers in base r follow the same rules as for decimal numbers.

Examples: addition, subtraction, and multiplication in base-2.

For more information study pages 18-20 in the text book. In Digital Computers arithmetic operations are done with the

binary number system (base-2) - Binary Arithmetic. In many cases binary subtraction is done in a special way by

binary addition. Why? It is much more simple to do it that way. One simple building block called adder can be implemented and used

for both binary addition and subtraction.

Carries:Augend:Addend:

Sum:

+

111 10110

01110 100100

Borrows:Minuend:

Subtrahend:Difference:

-

00110

11101

- 11 11101

00110 -10111

Multiplicand:Multiplier:

Product:

x 1010

101 1010

0000 1010 110010

+


35

Unsigned Binary Subtraction

Binary subtraction by 2’s complement addition Assume two n-bit unsigned numbers M and N, M - N can be done as follows: Add the 2’s complement of N to M. This performs the sum M + (2n - N) =

= M – N + 2n . If M ≥ N, the sum produces an end carry, 2n. We can discard it, leaving the

correct result M – N. If M < N, the sum does not produces an end carry since it is equal to

2n – (N - M), which is the 2’s complement of N – M. To obtain the correct result take the 2’s complement of the sum, i.e., 2n – (2n – (N - M)) = (N - M) and place a minus sign in front.

Examples:

What about binary subtraction by 1’s complement addition? I leave this for you as a home work

0101

0001 0110

(5) (2’s compl. of 15)(the sum)

+ 5

15-10

-

-1010 ( “-” 2’s compl. of sum )no carry correction is needed

1111

1011 1 1010

(15) (2’s compl. of 5)(the sum)

+ 15

510

-

discard carry


36

Signed Binary Addition/Subtraction

Signed binary addition using 2’s complement representation Assume two n-bit signed numbers M and N represented in signed-2’s

complement format. The sum M + N can be obtained as follows: Add M to N, including their sign bits to get the correct sum in signed-2’s

complement format. A carry out of the sign bit position is discarded. Examples:

Signed binary subtraction using 2’s complement representation Assume two n-bit signed numbers M and N represented in signed-2’s

complement format. The difference M - N can be obtained as follows: Take the 2’s complement of N (including the sign bit) and add it to M

(including the sign bit). A carry out of the sign bit position is discarded. Examples:

(- 9)(+ 5)(- 4)

+ 1|0111

0|0101 1|1100

discard

+(- 9)(- 5)(-14)

1|0111

1|1011 11|0010

(+ 9)(+ 5)(+14)

+ 0|1001

0|0101 0|1110

(+ 9)(- 5)(+ 4)

+ 0|1001

1|1011 10|0100

discard

(- 9)(+ 5)(-14)

- 1|0111

0|0101

1|0111

1|1011 11|0010

+(- 9)(- 5)(- 4)

- 1|0111

1|1011

1|0111

0|0101 1|1100

+

discard Fall 2007 Digital Techniques by André Deutz, Leiden University

37

Decimal Codes

The binary number system is the most natural system for a digital computer, but people are accustomed to the decimal system.

How to resolve this difference? Convert decimal numbers to binary, perform all arithmetic

calculations in binary, and then convert the binary result back to decimal.

You already know how to do this. Digital computers can do this as well, but:

We have to store the decimal numbers in the computer in a way that they can be converted to binary.

Since the computer can accept only binary values, we must represent the decimal digits by a code that contains 1’s and 0’s.


38

Binary Coded Decimals (BCD) (1)

The BCD code is the most commonly used code. Each decimal digit (0, 1, 2, …, 9) is coded by a 4-bit string (half a byte) called BCD digit.

A decimal number is converted to a BCD number by replacing each decimal digit of the number with the corresponding BCD digit code.

Example:(369)10 = ( 0011 0110 1001 )BCD = (101110001)2

3 6 9 A BCD number needs more bits than its

equivalent binary value. However, the advantages of using BCD are:

Computer input and output data are handled by people who use the decimal system.

BCD numbers are decimal numbers (not binary numbers) even though they are represented in bits.

Computers can store decimal numbers using BCD, convert the BCD numbers to binary, perform binary operations, and convert the result back to BCD.

Decimal Digit BCD Digit

0 0000

1 0001

2 0010

3 0011

4 0100

5 0101

6 0110

7 0111

8 1000

9 1001

Note: the binary combinations 1010 through 1111 are not used and have no meaning in the BCD code.


39

Converting a BCD number to a binary number(25)10 = (0010 0101)BCD = (0010)2 x 101 + (0101)2 x 100 =

= (0010)2 x (1010)2 + (0101)2 x (0001)2 =

= (10100)+(0101) = (11001)2

Converting a binary number to a BCD number

BCD Arithmetic Digital computers can performed arithmetic operations directly with

decimal numbers when they are stored in BDC format. How is this done? (study the text book or go to internet for information).

Binary Coded Decimals (BCD) (2)

Convert the number (11001)2 by dividing it to (1010)2 = (10)10

(11001)2 / (1010)2 = (0010)2 and Remainder = (0101)2 Least significant BCD digit

(0010)2 / (1010)2 = (0000)2 and Remainder = (0010)2 Most significant BCD digit

(11001)2 = ( 0010 0101 )BCD = (25)10


40

Other Useful Decimal Codes:Seven-Segment Code

Used to display numeric info on seven-segment displays. Seven-segment display:

7 LEDs (light emitting diodes), each one controlled by an input 1 means “on”, 0 means “off” Display digit “3”?

Set a, b, c, d, g to 1 Set e, f to 0

Decimal Digit

7- Segment Code

a b c d e f g

0 1 1 1 1 1 1 0

1 0 1 1 0 0 0 0

2 1 1 0 1 1 0 1

3 1 1 1 1 0 0 1

4 0 1 1 0 0 1 1

5 1 0 1 1 0 1 1

6 1 0 1 1 1 1 1

7 1 1 1 0 0 0 0

8 1 1 1 1 1 1 1

9 1 1 1 1 0 1 1d

a

b

c e

f g


41

Alphanumeric Codes

Many applications of digital computers require the handling of data consisting not only of numbers, but also of letters.

Alphanumeric character set of English includes: The 10 decimal digits The 26 letters of the alphabet (uppercase and lowercase letters) Several (more than three) special characters

We need to code these symbols The code must be binary – computers can handle only 0’s and 1’s We need binary code of at least seven bits (27 = 128 symbols)

American Standard Code for Information Interchange (ASCII) ASCII is a 7-bit standard code for representing the symbols of the

English language. Unicode

A 16-bit standard code for representing the symbols and ideographs for the world’s languages.


42

ASCII Code Table


Fall 2007 Digital Techniques by André Deutz, Leiden University 43

ASCII Character Code

• ASCII is a 7-bit code, commonly stored in 8-bit bytes.

• “A” is at 4116. To convert upper case letters to lower case letters, add 2016. Thus “a” is at 4116 + 2016 = 6116.

• The character “5” at position 3516 is different than the number 5. To convert character-numbers into number-numbers, subtract 3016: 3516 - 3016 = 5.

44

ASCII Code Table


45

Gray Codes


46

What is What?

How do you know whether binary bit string 00110001 represents an ASCII code with odd parity for the character ‘1’ , the positive number 49, or the positive number 31?

digital techniques instructor: dr. andré deutz office: room 116 office phone: 071 - 527 – 7071...

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