This document provides an overview of key topics related to computer data representation and binary number systems. It discusses how computers use binary switches to represent all data as strings of 0s and 1s. It also introduces different number systems like decimal, binary, octal and hexadecimal. The document explains how to convert between these number systems. Additionally, it covers binary arithmetic operations like addition, subtraction, multiplication and division. Finally, it discusses common units of data representation like bits, bytes and words, as well as coding methods such as BCD, EBCDIC and ASCII that are used to represent alphanumeric characters in binary.

1. Topics
Computer Switches
Number Systems
Converting form one number
system to another
Binary Arithmetic
Units of data representation
Coding methods

2.  Computers work in binary language.
 Consists of two numbers: 0 and 1.
 Everything a computer does is broken
down into a series of 0s and 1s.
 Switches: Devices inside the
computer that can be flipped between
these two states: 1 or 0, on or off.

3.  Number systems are organized ways to
represent numbers.
 Each number in one system has a
corresponding number in another.
• There are different number systems. Some
of them are:-
– Decimal – base(10) 0-9
– Binary- base(2) 0,1
– Octal- base(8) 0-7
– Hexadecimal- base(16) 0-9,A,B,C,D,E,F

4.  Describes a number as powers of 2.
 Also referred to as base 2 numbering
system.
 Used to represent every piece of data
stored in a computer: all of the numbers,
letters, and instructions are a series of 0s
and 1s.

5.  Describes a number as powers of 10.
 Also referred to as base 10 numbering
system.
 It uses 10 symbols 0-9 to represent
numbers;
 Computers used binary number system to
represent every piece of data stored in a
computer and Humans understand
decimal number systems easily.

6.  Conversion from Decimal to Binary
1. (37)(10) = ………(2)
2. (56)(10) = ………(2)
3. (15.75)(10) = ………(2)
4. (27.25)(10) = ………(2)

7. 1. (10011)(2)= ……..(10)
2. (1001001)(2)= ……..(10)
3. (11001.11)(2)= ……..(10)
4. (1100101.01)(2)= ……..(10)

8.  Computer understands only the language of
binary numbers. Therefore, the machine
performs what is called binary arithmetic
(binary computation).
1. Binary Addition
2. Binary Subtraction
3. Binary Multiplication
4. Binary Division

9.  The binary addition rules may be written as
follows:
• 0+0=0
• 0+1=1
• 1+0=1
• 1+1=0 plus a carry of 1 into the next position
• 1+1+1=1 plus a carry of 1 into the next position

10. • Example1. 6+7 =13
110 ----> 6
+ 111 ----> 7
…… ---->13
• Example2. 19+31+10=60
10011------->19
+ 11111------->31
+ 1010------->10
……… ------>60
• Example3. 11001.011 + 111.110 =………..

11.  It operates by the same rule as decimal subtraction.
The rule is as follows;
 0-0=0
 1-0=1
 1-1=0
 10-1=1
 Example1.
11100 28 101101 45 11001.011
- 11010 -26 - 111 -7 - 111.110
…….… = 2 ……… = 38 ………….

12.  It is a very simple process that operates by the
following obvious rulers:
(a) Multiplying any number by 1 rules the
multiplicand unchanged
 0x1=0
 1x1=1
(b) Multiplying any number by 0 produces 0
 0x0=0
 1x0=0
 Example1.
101 110.01
x 10 x 10.1
……… .……....

13.  That is, the process for dividing one binary
number (the dividend) by another (the divisor)
is based on the rules for binary subtraction and
multiplication and Similar to decimal division.
 Example1.
1111 ÷ 101 = …….
 Example2.
1111101 ÷ 11001 = ……

14.  Bit
 Binary digit
 0 or 1
 Bits are the smallest units
 Byte
 Eight bits
 The basic unit of data representation in a
computer system;
 Word
 A combination of bytes, then form a
“word”.
 Word refers the number of bits that a computer
process at a time or a transmission media
transmits at a time.
 The large the word length a computer has the
more powerful and faster it is.
OFF
0
ON
1
Microchip
Switch

15. NAME ABBREVIATION NUMBER OF
BYTES
RELATIVE SIZE
Byte B 1 byte Can hold one character of data.
Kilobyte KB 1,024 bytes Can hold 1,024 characters or about half
of a typewritten page double-spaced.
Megabyte MB 1,048,576 bytes A floppy disk holds approximately 1.4
MB of data, or approximately 768 pages
of typed text.
Gigabyte GB 1,073,741,824 bytes Approximately 786,432 pages of text.
Since 500 sheets of paper is
approximately 2 inches, this represents
a stack of paper 262 feet high.
Terabyte TB 1,099,511,627,776
bytes
This represents a stack of typewritten
pages almost 51 miles high.
Petabyte PB 1,125,899,906,842,624
bytes
The stack of pages is now 52,000 miles
high, or about one-fourth the distance
from the Earth to the moon.

16.  In previous sections we introduced the most common
types of binary-coded data found in digital computers.
 Other binary codes for decimal numbers and
alphanumeric characters are sometimes used.
 Digital Computers also employ other binary codes for
special applications.
BCD (Binary Coded Decimal)
EBCDIC (Extended Binary Coded Decimal
Interchange Code )
ASCII (American Standard Code for
Information Interchange)

17.  There are two types of BCD coding techniques
used before.
a) 4 bits BCD and
b) 6 bits BCD
BCD (4 -bits)
 The 4 bit BCD, which represent any digit of
decimal number by four bits of binary
numbers.
 If you want to represent 219 using 4 bit BCD
you have to say 0010 0001 1001
 Ex. 546= ……….

18.  It uses 6-bits to code a Character (2 for zone bit and 4 for
digit bit)
 It can represent 26 = 64 characters (10 digits, 26 capital
characters and some other special characters).
 Some Coding Examples
Character zone zone (2 Bit) Digit (4 Bit)
0-9 0 0-9
A-I 3 1-9
J-R 2 1-9
S-Z 1 2-9
Example 1. Represent Character A using 6-bits BCD
A 11 0001
A = 110001
J = ……… 2 =……….. D =………………..

19.  It is an 8-bit coding scheme: (00000000 – 11111111)
 It accommodates to code 28 or 256 different characters
 It is a standard coding scheme for the large computers.
 Coding Example:
Character zone (4 Bit) Digit (4 Bit)
0-9 15 0-9
a-i 8 1-9
j-r 9 1-9
s-z 10 2-9
A-I 12 1-9
J-R 13 1-9
S-Z 14 2-9
Example 1. Represent Character A using EBCIDIC
A 1100 0001
A= 11000001
a=………… Z=………………
2 = ……….. d =……………….

20.  Used widely before the introduction of ASCII-8 (the Extended
ASCII)
 Uses 7 bits to represent a character;
 With the seven bits, 27(or 128) different characters can be coded
(0000000-1111111)
 Coding examples:
Character zone (3 bit) digit (4 bit)
0-9 3 0-9
A-O 4 1-15
P-Z 5 0-10
a- o 6 1-15
p- z 7 0-10
Example 1. Represent Character A using ASCII-7
A 100 0001
A= 1000001
a = ……….. E =………………….
2 = ……….. r =…………………

21. Any Question?