1. Number Systems & Logic Gates Day 1

2. Computerized ? Characters/ Words Colors Sounds Feelings

3. Data Representation How Data is Stored ( Either 0 or 1 )
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”

4. Data Representation byte – 8 bits1
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”.

5. 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

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

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

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

9. Binary Strings Thus, 4 bit Binary String 24=16 0000 - A 1000 - J
B K
C L
D M
E N
G O
H P
I Q

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

11. Binary Coded Decimal (BCD)
The decimal number 109 can be coded as
(BCD)
(BCD)
(BCD)

12. Binary Strings Thus, 5 bit Binary String 25=32

13. 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).

14. Character Codes – ASCII
Number ASCII Letter ASCII A B C D E F G H I

15. Character Codes – ASCII
Letter ASCII Letter ASCII J K L M N O P Q R S T U V W X Y Z

16. 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”.

17. 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
digit
zone 1 2 3 4 5 6 7 8

18. 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

19. Character Codes – EBCDIC
Number EBCDIC Letter EBCDIC A B C D E F G H I

20. Character Codes – EBCDIC
Letter EBCDIC Letter EBCDIC J K L M N O P Q R S T U V W X Y Z

21. 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)

22. 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

23. Decimal Number System Base (Radix) 10
Digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
e.g
The magnitude representation by a digit is decided by the
position of the digit within the number.
103= = =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.

24. Binary Number System Base (Radix) 2 Digits 0, 1 e.g. 11102 1 1 1 0
23=8 22=4 21=2 20=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.