Number Systems Logic Gates Day 1 Computerized Characters

Number Systems & Logic Gates Day 1

Computerized ? Characters/ Words Colors Sounds Feelings Characters/ Words Colors Sou

Data Representation How Data is Stored BIT – B i n a r y d i g I T ( Either 0 or 1 ) 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 Representation byte – 8 bits 1 1 0 1 • 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

Binary Strings n bit binary string represents 2 n different Binary strings. Thus, 1 bit Binary String 21=2 0 -A 1 -B

Binary Strings Thus, 2 bit Binary String 22=4 00 - A 01 - B 10 - C 11 - D

Binary Strings Thus, 3 bit Binary String 23=8 000 - A 001 - B 010 - C 011 - D 100 - E 101 - F 110 - G 111 - H

Binary Strings Thus, 4 bit Binary String 24=16 0000 - A 0001 - B 0010 - C 0011 - D 0100 - E 0101 - G 0110 - H 0111 - I 1000 - J 1001 - K 1010 - L 1011 - M 1100 - N 1101 - O 1110 - P 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 - 8 0001 - 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 00010001

Binary Strings Thus, 5 bit Binary String 6 bit Binary String 7 bit Binary String 8 bit Binary String 25=32 26=64 27=128 28=256

7 bit ASCII code The 7 bit ASCII (American Standard Code for Information Interchange) code was originally proposed by the American National Standard Institute (ANSI) and was developed by the International Organization for Standardization (ISO) and the Committee Consultants of International Telephone and Telegraphic (CCITT) into the international Alphabet (IA).

Character Codes – ASCII Number ASCII 0 1 2 3 4 5 6 7 8 9 0110000 0110001 0110010 0110011 0110100 0110101 0110110111 0111000 0111001 Letter A B C D E F G H I ASCII 1000001 1000010 1000011 1000100 1000101 1000110 1000111 1001000 1001001

Character Codes – ASCII Letter ASCII J K L M N O P Q R 1001010 1001011 1001100 1001101 1001110 1001111 1010000 1010001 1010010 Letter S T U V W X Y Z ASCII 1010011 1010100 101010110 1010111 1011000 1011001 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 • Each 8 -bit byte is divided into two portions – zone portion and digit portion – digit portion is based on the binary number system zone digit 0 0 1 1 1 8 7 6 5 4 3 2 1

Character Codes – EBCDIC • 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

Character Codes – EBCDIC Number EBCDIC 0 1 2 3 4 5 6 7 8 9 11110000 11110001 11110010 11110011 11110100 11110101 11110110 11110111 11111000 11111001 Letter EBCDIC A B C D E F G H I 11000001 11000010 11000011 11000100 11000101 11000110 11000111 11001000 11001001

Character Codes – EBCDIC Letter EBCDIC J K L M N O P Q R 11010001 11010010 11010011 11010100 11010101 11010110 11010111 11011000 11011001 Letter EBCDIC S T U V W X Y Z 11100010 11100011 11100100 11100101 11100110 11100111 11101000 11101001

How Capacity is Expressed Kilobyte (KB) is about 1000 bytes 1024 Bytes (210 bytes) Megabyte (MB) is about 1 million bytes 1024 KB (220 bytes) Gigabyte (GB) is about 1 billion bytes 1024 MB (230 bytes) Terabyte (TB) is about 1 trillion bytes 1024 GB (240 bytes)

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. 5 103=1000 6 102=100 2 5 101=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 3 2 =8 1 2 2 =4 1 1 2 =2 0 0 2 =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.