Number Systems & Logic Gates Day 1

Number Systems & Logic GatesDay 1

Computerized ?

Characters/ Words

Colors

Sounds

Feelings

Characters/ Words

Colors

Sou

Data Representation

BIT – B i n a r y d i g I T ( Either 0 or 1 )

How Data is Stored

Basic unit for storing data in main computer memory is the bit. A bit can represent one of only two values.

bit 0 is said to be “off”bit 1 is said to be “on”

Data Representationbyte – 8 bits 10111011

• Many computers use a combination of 8 bits (called a byte) as a unit for storing data.

• Thus a byte is a location in the computer main memory consists of 8 adjacent bits.

• When a character is entered from the keyboard, the computer interprets the character and stores it as a series of bits being “on” and “off”.

Binary String

• Collection of bits/ bit sequence is called as a Binary String.

Example

1,0,1

1,1,1,0,1,1

1,0,1,0,1,.0,1,0

Binary Strings

n bit binary string represents 2n different

Binary strings.

Thus,

1 bit Binary String 21=2

0 - A

1 - B

Binary StringsThus,


00 - A

01 - B

10 - C

11 - D

Binary StringsThus,


000 - A 100 - E

001 - B 101 - F

010 - C 110 - G

011 - D 111 - H

Binary StringsThus,4 bit Binary String 24=16

0000 - A 1000 - J0001 - B 1001 - K

0010 - C 1010 - L 0011 - D 1011 - M

0100 - E 1100 - N0101 - G 1101 - O0110 - H 1110 - P0111 - I 1111 - Q

Binary Coded Decimal (BCD)BCD is a 4-bit code used for coding numerical values only.4 bit Binary String 24=16

0000 - 0 1000 - 80001 - 1 1001 - 9

0010 - 2 0011 - 3

0100 - 4 0101 - 5 0110 - 6 0111 - 7

Binary Coded Decimal (BCD)

The decimal number 109 can be coded as

1- 0001 (BCD)

0- 0000 (BCD)

9- 1001 (BCD)

1 0 9

0001 0000 1001

0001000010001

Binary Strings

Thus,





7 bit ASCII codeThe 7 bit ASCII (American Standard Codefor Information Interchange) code wasoriginally proposed by the American NationalStandard Institute (ANSI) and was developed by the International Organization forStandardization (ISO) and the Committee Consultants of International Telephone andTelegraphic (CCITT) into the internationalAlphabet (IA).

Character Codes – ASCII

001100001

01100012

01100103

01100114

01101005

01101016

01101107

01101118

01110009

0111001

Number ASCII Letter ASCII

A1000001B

1000010C

1000011D

1000100E

1000101F

1000110G

1000111H

1001000I

1001001

Character Codes – ASCII

J1001010K

1001011L

1001100M

1001101N

1001110O

1001111P

1010000Q

1010001R

1010010

Letter ASCII Letter ASCII

S1010011T

1010100U

1010101V

1010110W

1010111X

1011000Y

1011001Z

1011010

EBCDIC

Eight bit EBCDIC (Extended Binary Coded

Decimal Interchange Code) is used by large

IBM computers and compatible equipment

(IBM Personal computers use ASCII).

EBCDIC is sometimes called “8 bit ASCII”.

Character Codes – EBCDIC

digitzone

111011110000

123455667788

• Each 8-bit byte is divided into two portions– zone portion and digit portion– digit portion is based on the binary number

system


• Numbers– All zone bits “on” and binary digits

• Letters (A-I)– Two zone bits (7, 8) “on” and binary digits

• Letters (J-R)– Three zone bits (5, 7, 8) “on” and binary digits

• Letters (S-Z)– Three zone bits (6, 7, 8) “on” and binary digits


0111100001

111100012

111100103

111100114

111101005

111101016

111101107

111101118

111110009

11111001

Number EBCDIC Letter EBCDIC

A11000001B

11000010C

11000011D

11000100E

11000101F

11000110G

11000111H

11001000I

11001001

Character Codes – EBCDIC Letter EBCDIC Letter EBCDIC

J11010001K

11010010L

11010011M

11010100N

11010101O

11010110P

11010111Q

11011000R

11011001

S11100010T

11100011U

11100100V

11100101W

11100110X

11100111Y

11101000Z

11101001

Kilobyte (KB) is about 1000 bytes1024 Bytes (210 bytes)

Megabyte (MB) is about 1 million bytes1024 KB (220 bytes)

Gigabyte (GB) is about 1 billion bytes1024 MB (230 bytes)

Terabyte (TB) is about 1 trillion bytes1024 GB (240 bytes)

How Capacity is Expressed

Radix Number Systems

• Each number system has a number of different set of digits which is called the radix or the base of the number system.

• Decimal Base=10

• Binary Base=2

• Octal Base=8

• Hexadecimal (Hex) Base=16

Decimal Number System

Base (Radix) 10

Digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

e.g. 562510

The magnitude representation by a digit is decided by the

position of the digit within the number.

5 6 2 5

103=1000 102=100 101=10 100=1

For example the digit 5 in the left-most position of 5625 counts for

5000 and the digit 2 in the second position counts for 20.

Binary Number System

Base (Radix) 2

Digits 0, 1

e.g. 11102

1 1 1 0

23=8 2

2=4 2

1=2 2

0=1

The digit 1 in the third position from the right represents the value

4 and the digit 1 in the fourth position from the right represents

the value 8.

Number Systems & Logic Gates Day 1

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