The document explains the concepts of data representation in computers, focusing on binary and decimal numbering systems. It details how data is organized in databases, the significance of character sets like ASCII, and methods for converting between decimal and binary numbers. Additionally, it covers the properties of binary numbers, such as weight, and provides examples of conversions.

1. Animation

10. Example

11. Create a flowchart on How to go to school.

12. Peg Bar

14. Paper and
Cel Punch

18. Animation Disc

19. Decimal and Binary System
Data is defined in a formalized manner as representing
facts , concepts, or instructions that should be suitable for
human or electronic machine communication,
interpretation, or processing. Data is represented with the
help of characters such as alphabets (A-Z, a-z), digits (0-9)
or special characters (+,-,/,*,<,>,= etc.) Data in its utmost
whole is normally called a database. A database is a
collection of files, a file is made up of records, a record is
made up of fields, a field is made up of characters, a
character is made up of bytes and a byte is made up of
bits (bit is short form for binary digit). When data is
organized into a database, it becomes easy to access and
manipulate.

20. The ASCII
Character
Set

21. The ASCII Character Set
All are based on ASCII, the character sets used in modern computers, in HTML,
and on the Internet. Always remember that the computer reads only 1s and 0s,
it is important to know how these data are converted into 1s and 0s using the
ASCII code. Conversion of binary to decimal (base-2 to base-10) numbers and
back is an important concept to understand, since the binary numbering
system forms the basis for all computers and digital systems. The decimal or
“denary” counting system uses the Base-of-10 numbering system where each
digit in a number takes on one of ten possible values, called “digits”, from 0 to
9, eg. 21310 (Two Hundred and Thirteen). But as well as having 10 digits ( 0
through 9 ), the decimal numbering system also has the operations of addition
( + ), subtraction ( – ), multiplication ( × ) and division ( ÷ ).

22. Repeated Division-by-2 Method
An easy method of converting
decimal to binary number
equivalents is to write down the
decimal number and to continually
divide-by-2 (two) to give a result
and a remainder of either a “1” or a
“0” until the final result equals zero.
For example: Convert the decimal
number 29410 into its binary
number equivalent.

23. Repeated Division-by-2 Method
We will stop when get a quotient of 0. This
divide-by-2 decimal to binary conversion
technique gives the decimal number 29410 an
equivalent of 1001001102 in binary, reading
from right to left. This divide-by-2 method will
also work for conversion to other number
bases. Then we can see that the main
characteristics of a Binary Numbering System
are that each "binary digit" or "bit" has either a
value of "1" or "0" with each bit having a weight
or value double that of its previous bit starting
from the lowest or least significant bit (LSB) and
this is called the "sum-of-weights" method.

24. The Binary Numbering System
In all digital and computer-based systems, the
binary numbering system is the most fundamental
numbering system, and binary numbers follow the
same set of rules as the decimal numbering
system. But unlike the decimal system that uses
ten powers, the binary numbering system operates
on two powers giving a binary conversion from
base-2 to base-10 to decimal. Digital logic and
computer systems use just two values or states to
represent a condition, a logic level “1” or a logic
level “0”, and each “0” and “1” is considered to be a
single digit in a Base-of-2 (bi) or “binary numbering
system”.

25. The Binary Numbering System
In the binary numbering system, a binary number such as 101100101 is
expressed with a string of “1’s” and “0’s” with each digit along the string
from right to left having a value twice that of the previous digit. But as it is a
binary digit it can only have a value of either “1” or “0” therefore, q is equal
to “2” (0 or 1) with its position indicating its weight within the string. As the
decimal number is a weighted number, converting from decimal to binary
(base 10 to base 2) will also produce a weighted binary number with the
right-hand most bit being the Least Significant Bit or LSB, and the left-hand
most bit being the Most Significant Bit or MSB, and we can represent this as:

26. The Binary Numbering System
Representation of a Binary Number

27. The Binary Numbering System
We've shown above that in the decimal number system the weight of
each digit increases by a factor of 10 from right to left. In the system of
binary numbers the weight of each digit increases as shown by a factor
of 2. Then the first digit weighs 1 (20), the second digit weighs 2 (21),
the third weighs 4 (22), the fourth weighs 8 (23) etc.
So for example, converting a Binary to Decimal number would be:

28. The Binary Numbering System
So for example, converting a Binary to Decimal number would be:

29. The Binary Numbering System
By adding together ALL the decimal number values from right to left at the
positions that are represented by a “1” gives us: (256) + (64) + (32) + (4) + (1) =
35710 or three hundred and fifty seven as a decimal number. Then, we can
convert binary to decimal by finding the decimal equivalent of the binary
array of digits 1011001012 and expanding the binary digits into a series with
a base of 2 giving an equivalent of 35710 in decimal or denary. Note that in
number conversion systems “subscripts” are used to indicate the relevant
base numbering system, 10012 = 910. If no subscript is used after a number,
then it is generally assumed to be decimal. On the other hand, to check if
your conversion is correct let us have the binary to decimal conversion

34. based on the video that we watched, write an
essay about animation in the Philippines and
how it inspired you to be an animator in the
future.

35. Answer
1. 101010100
2. 100011101
3. 10111101
4. 100110101
5. 110110000

37. Binary to Decimal Summary
• A “BIT” is the abbreviated term derived from BInary digiT
• A binary system has only two states, Logic “0” and Logic “1” giving a base of 2
• A decimal system uses 10 different digits, 0 to 9 giving it a base of 10
• A binary number is a weighted number whose weighted value increases from
right to left
• The weight of a binary digit doubles from right to left.
• A decimal number can be converted to a binary number by using the sum-of-
weights method or the repeated division-by-2 method
• When we convert numbers from binary to decimal, or decimal to binary,
subscripts are used to avoid errors

39. Using the ASCII table, convert Bagong
Silang High School into binary.

40. Convert the following from decimal to binary or vice versa. Show your solution. 6. 65410 to _________ 2
7. 178610 to _________ 2
8. 34510 to _________ 2
9. 1110011002 to ________ 10
10. 11111111112 to ________ 10