dld lecture module 03

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Digital Logic & Design

Dr. Sajjad Ahmed Nadeem

Department of Computer Science & IT University of Azad Jammu & Kashmir

Muzaffarabad

Module 03

� Computer Codes.

� BCD.

� EBCDIC.

� ASCII.

� Assignment-2

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Data Types

Computer Codes (1)

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Computer Codes (2)

Binary-Coded Decimal (BCD)

� Four bits per digit Digit Bit pattern

0 0000

1 0001

2 0010

3 0011

4 0100

5 0101

6 0110

7 0111

8 1000

9 1001

Note: the following bit

patterns are not used:

1010

1011

1100

1101

1110

1111

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Example

� 709310 = ? (in BCD)

7 0 9 3

0111 0000 1001 0011

Chapter 1 8

Warning: Conversion or Coding?

� Do NOT mix up conversion of a decimal number to a binary number with coding a decimal number with a BINARY CODE.

� 1310 = 11012 (This is conversion)

� 13 ⇔ 0001|0011 (This is coding)

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Addition-Example-1

410 0100

+510 +0101 _________________

910 1001

410 0100

+810 +1000 _________________

1100

+0110

_________________

1210 1 0010

Addition-Example-2

1 1

18410 0001 1000 0100

+57610 0101 0111 0110 ______________________________________________

Binary Sum 0111 10000 1010

Add 6 0110 0110 ______________________________________________

76010 0111 0110 0000

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Other Decimal Codes-Binary Codes for Decimal Digits

Decimal 8,4,2,1 Excess3 8,4, - 2, - 1 Gray

0 0000 0011 0000 0000

1 0001 0100 0111 0100

2 0010 0101 0110 0101

3 0011 0110 0101 0111

4 0100 0111 0100 0110

5 0101 1000 1011 0010

6 0110 1001 1010 0011

7 0111 1010 1001 0001

8 1000 1011 1000 1001

9 1001 1 100 1111 1000

BCD 2421

0000

0001

0010

0011

0100

1011

1100

1101

1110

1111

Other Decimal Codes-Binary Codes for Decimal Digits

• Excess-3

• Is unweighted code

• Is obtained from the corresponding values + 3

• has been used in some older computers.

• Some digits in 2421 can be coded in two possible

ways e.g. 4 = 0100 and 4=1010

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� What special property does the Gray code have in relation to adjacent decimal digits?

GRAY CODE – Decimal

Decimal 8,4,2,1 Gray

0 0000 0000 1 0001 0100

2 0010 0101

3 0011 0111

4 0100 0110

5 0101 0010

6 0110 0011

7 0111 0001

8 1000 1001

9 1001 1000

EBCDIC

� Extended BCD Interchange Code

� 8-bit code (28 = 256 different characters)

� Developed by IBM

� Rarely used today

� IBM mainframes only

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Coding of Alphabetic and Numeric Characters in EBCDIC

Coding of Alphabetic and Numeric Characters in EBCDIC

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EBCDIC

The Problem

� Representing text strings, such as “Hello, world”, in a computer

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ASCII

ASCII-7 Features

� 7-bit code

� 8th bit is unused (or used for a parity bit)

� 27 = 128 codes

� Two general types of codes: ◦ 95 are “Graphic” codes (displayable on a console)

◦ 33 are “Control” codes (control features of the console or communications channel)

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ASCII-7 Chart

000 001 010 011 100 101 110 1110000 NULL DLE 0 @ P ` p0001 SOH DC1 ! 1 A Q a q

0010 STX DC2 " 2 B R b r0011 ETX DC3 # 3 C S c s

0100 EDT DC4 $ 4 D T d t0101 ENQ NAK % 5 E U e u0110 ACK SYN & 6 F V f v0111 BEL ETB ' 7 G W g w1000 BS CAN ( 8 H X h x1001 HT EM ) 9 I Y i y

1010 LF SUB * : J Z j z1011 VT ESC + ; K [ k {

1100 FF FS , < L \ l |1101 CR GS - = M ] m }1110 SO RS . > N ^ n ~1111 SI US / ? O _ o DEL






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Most significant bit

Least significant bit






e.g., ‘a’ = 1100001

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95 Graphic codes






33 Control codes






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Alphabetic codes






Numeric codes






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Punctuation, etc.

“Hello, world” Example

= = = = = = = = = = = =

Binary 01001000 01100101 01101100 01101100 01101111 00101100 00100000 01110111 01100111 01110010 01101100 01100100

Hexadecimal 48 65 6C 6C 6F 2C 20 77 67 72 6C 64

Decimal 72 101 108 108 111 44 32 119 103 114 108 100

H e l l o , w o r l d

= = = = = = = = = = = =

= = = = = = = = = = = =

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Common Control Codes

� CR 0D carriage return

� LF 0A line feed

� HT 09 horizontal tab

� DEL 7F delete

� NULL 00 null

Hexadecimal code






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Terminology

� Learn the names of the special symbols

◦ [ ] brackets

◦ { } braces

◦ ( ) parentheses

◦ @ commercial ‘at’ sign

◦ & ampersand

◦ ~ tilde






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Coding of Alphabetic and Numeric Characters in ASCII


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PARITY BIT Error-Detection Codes

� Redundancy (e.g. extra information), in the form of extra bits, can be incorporated into binary code words to detect and correct errors.

� A simple form of redundancy is parity, an extra bit appended onto the code word to make the number of 1’s odd or even. Parity can detect all single-bit errors and some multiple-bit errors.

� A code word has even parity if the number of 1’s in the code word is even.

� A code word has odd parity if the number of 1’s in the code word is odd.

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4-Bit Parity Code Example � Fill in the even and odd parity bits:

� The codeword "1111" has even parity and the codeword "1110" has odd parity. Both can be used to represent 3-bit data.

Even Parity Odd Parity Message - Parity Message - Parity

000 - 000 - 001 - 001 - 010 - 010 - 011 - 011

- 100 - 100 - 101 - 101

- 110 - 110 - 111 - 111 -

Assignment-2

BCD subtraction

UNICODE

dld lecture module 03

Education