Communication and Network Fundamentals

1. Data Representation

Key Concept: Computers use binary language (comprising 0s and 1s) to represent data.
The Process: Whatever input a user gives to a computer (letters, numbers, symbols, audio, or video) or whatever output is received, it must first be converted into binary language.
Definition: The process of converting data and presenting it in the form of 0s and 1s is known as Data Representation.

2. Number System (Introduction)

Definition: A Number System is a collection of various types of numbers used to express data or instructions within a computer.
Internal Processing: Computers can be fed data in different number systems, but internally, the computer exclusively uses binary language to perform any task or operation.

3. Types of Number Systems

There are four primary types of number systems used by computer systems:

Binary Number System
Decimal Number System
Octal Number System
Hexa-decimal Number System

I. Binary Number System

Base (Radix): 2 (because it uses exactly two digits).
Symbols Used: 0 (Zero) and 1 (One).
Mechanism (Switch Concept): It acts like a switch with only two states:
- 0 (Zero): Represents OFF.
- 1 (One): Represents ON.
- No third state is possible in this system.
Positional Value: Moving from right to left, the positional values double sequentially (e.g., 1, 2, 4, 8, 16, 32, 64) and can be written as powers of 2 ($2^0, 2^1, 2^2, 2^3...$).
Binary Point (Fractions): To the right of a binary point, positional values decrease as negative powers of 2 ($2^{-1}, 2^{-2}, 2^{-3}...$).

II. Decimal Number System

Base: 10.
Symbols Used: Ten symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
Usage: This is the standard number system used in our daily lives.
Positional Value: Moving from right to left, the positional value increases in powers of 10.
- Positions: Units ($10^0$), Tens ($10^1$), Hundreds ($10^2$), Thousands ($10^3$), etc..
- To the right of the decimal point, values decrease as negative powers of 10 ($10^{-1}, 10^{-2}...$).
Example calculation of $(3437)_{10}$:
- $7 \times 10^0 = 7 \times 1 = 7$
- $3 \times 10^1 = 3 \times 10 = 30$
- $4 \times 10^2 = 4 \times 100 = 400$
- $3 \times 10^3 = 3 \times 1000 = 3000$
- Total = $3437$

III. Octal Number System

Base: 8.
Symbols Used: Eight digits: 0, 1, 2, 3, 4, 5, 6, and 7.
Usage: It is mainly used in microcomputers and is highly convenient for writing binary numbers in a shorter, more compact format.
Positional Value: Moving from right to left, the value increases by multiples of 8 ($8^0, 8^1, 8^2...$).
Example calculation of $(144)_8$:
- $4 \times 8^0 = 4 \times 1 = 4$
- $4 \times 8^1 = 4 \times 8 = 32$
- $1 \times 8^2 = 1 \times 64 = 64$
- Total = $(100)_{10}$
Notation Rule: To clearly identify a number system, the number is enclosed in parentheses, and its base is written as a subscript on the right side (e.g., $(144)_8$).

IV. Hexa-decimal Number System

Base: 16.
Meaning: Formed by combining "Hexa" (meaning 6) and "Decimal" (meaning 10).
Symbols Used: A total of sixteen symbols:
- Numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
- Alphabets: A, B, C, D, E, F (To avoid confusion with separate digits, letters represent values 10 through 15).
  - (A=10, B=11, C=12, D=13, E=14, F=15).
Positional Value: Moving from right to left, the value increases by multiples of 16 ($16^0, 16^1, 16^2...$).
Example calculation of $(F6A4)_{16}$:
- $4 \times 16^0 = 4 \times 1 = 4$
- $A (10) \times 16^1 = 10 \times 16 = 160$
- $6 \times 16^2 = 6 \times 256 = 1536$
- $F (15) \times 16^3 = 15 \times 4096 = 61440$
- Total = $(63140)_{10}$

4. Quick Revision Tables

Table 1: Classification of Number Systems

Number System	Base	Digits/Symbols Used	Key Usage
Binary	2	0, 1	Internal computer language / Switch states (ON/OFF)
Octal	8	0, 1, 2, 3, 4, 5, 6, 7	Shortening binary / Microcomputers
Decimal	10	0, 1, 2, 3, 4, 5, 6, 7, 8, 9	Daily life arithmetic
Hexa-decimal	16	0-9 and A-F (where A=10...F=15)	Expressing very large numbers compactly

Table 2: Number System Conversion (First 16 Numbers Equivalent)

(Any number can be written across any number system)

Decimal (Base 10)	Binary (Base 2)	Octal (Base 8)	Hexa-decimal (Base 16)
0	000	0	0
1	001	1	1
2	010	2	2
3	011	3	3
4	100	4	4
5	101	5	5
6	110	6	6
7	111	7	7
8	1000	10	8
9	1001	11	9
10	1010	12	A
11	1011	13	B
12	1100	14	C
13	1101	15	D
14	1110	16	E
15	1111	17	F

Source data mapped from. Note: The original table displays 3-bit binary for octal translations up to 7, and expands to 4-bits for larger decimal outputs.

1. Introduction to Number System Conversions

Need for Conversion: Users input data in the Decimal Number System, which the computer must convert into a system it finds convenient to process (like Binary).
System Usage: A digital computer system typically uses three or four different number systems at the same time, making it necessary to convert them back and forth.

2. Conversion of Decimal System to Other Number Systems

Converting a decimal number to another base (Binary, Octal, or Hexadecimal) requires different rules for the Integer (whole number) part and the Fraction (decimal point) part.

Rule 1: Converting Decimal Integers (Whole Numbers)

To convert a decimal integer to any other number system, use the Repeated Division Method:

Divide the decimal number by the Base (Radix) of the target number system (e.g., 2 for Binary, 8 for Octal, 16 for Hexadecimal).
Write down the Remainder on the right side and divide the new Quotient again by the target Base.
Continue this division process until the Quotient becomes zero (0).
Final Answer: Write all the collected remainders in reverse order (from bottom to top) to get the converted integer.

Rule 2: Converting Decimal Fractions (Numbers after the point)

To convert a decimal fraction to any other number system, use the Repeated Multiplication Method:

Multiply the decimal fraction by the Base of the target number system (e.g., 2, 8, or 16).
Write the resulting Integer part (whole number) on the right side.
Take the remaining fraction part and multiply it by the target Base again.
Continue this process until the fractional part becomes zero (0) or until you reach the desired number of decimal places.
Final Answer: Write the collected integers in forward order (from top to bottom) after the target system's decimal point.

3. Examples of Decimal Conversions

I. Decimal to Binary (Base 10 to Base 2)

Example: Convert $(53.6875)_{10}$ into Binary.

Step A: Integer Part (53)
- $53 \div 2 = 26$ (Remainder 1)
- $26 \div 2 = 13$ (Remainder 0)
- $13 \div 2 = 6$ (Remainder 1)
- $6 \div 2 = 3$ (Remainder 0)
- $3 \div 2 = 1$ (Remainder 1)
- $1 \div 2 = 0$ (Remainder 1)
- Result (Bottom to Top): $(110101)_2$
Step B: Fraction Part (0.6875)
- $0.6875 \times 2 = 1.3750$ (Integer 1)
- $0.3750 \times 2 = 0.7500$ (Integer 0)
- $0.7500 \times 2 = 1.5000$ (Integer 1)
- $0.5000 \times 2 = 1.0000$ (Integer 1)
- Result (Top to Bottom): $(.1011)_2$
Final Answer: $(110101.1011)_2$

II. Decimal to Octal (Base 10 to Base 8)

Example: Convert $(423.03125)_{10}$ into Octal.

Step A: Integer Part (423)
- $423 \div 8 = 52$ (Remainder 7)
- $52 \div 8 = 6$ (Remainder 4)
- $6 \div 8 = 0$ (Remainder 6)
- Result (Bottom to Top): $(647)_8$
Step B: Fraction Part (0.03125)
- $0.03125 \times 8 = 0.250$ (Integer 0)
- $0.250 \times 8 = 2.00$ (Integer 2)
- Result (Top to Bottom): $(.02)_8$
Final Answer: $(647.02)_8$

III. Decimal to Hexadecimal (Base 10 to Base 16)

Example: Convert $(2863.225)_{10}$ into Hexadecimal.

Step A: Integer Part (2863)
- $2863 \div 16 = 178$ (Remainder 15 = F)
- $178 \div 16 = 11$ (Remainder 2)
- $11 \div 16 = 0$ (Remainder 11 = B)
- Result (Bottom to Top): $(B2F)_{16}$
Step B: Fraction Part (0.225)
- $0.225 \times 16 = 3.6$ (Integer 3)
- $0.6 \times 16 = 9.6$ (Integer 9)
- Result (Top to Bottom): $(.39)_{16}$
Final Answer: $(B2F.39)_{16}$

4. Introduction: Binary to Other Number Systems

(i) Binary (Integer) to Decimal Conversion:

To convert any binary number back into the decimal system, you must multiply each individual bit by its respective positional value (powers of 2).
After multiplying, you add all the resulting values together to get the final decimal equivalent. (Note: Detailed examples of this will be in the next section of your material).

5. Quick Revision Tables

Table: Rules for Converting Decimal to Other Systems

Target System	Target Base	Rule for Integer Part	Rule for Fractional Part	Reading Direction
Binary	2	Divide by 2 repeatedly	Multiply by 2 repeatedly	Int: Bottom $\rightarrow$ Top Frac: Top $\rightarrow$ Bottom
Octal	8	Divide by 8 repeatedly	Multiply by 8 repeatedly	Int: Bottom $\rightarrow$ Top Frac: Top $\rightarrow$ Bottom
Hexadecimal	16	Divide by 16 repeatedly	Multiply by 16 repeatedly	Int: Bottom $\rightarrow$ Top Frac: Top $\rightarrow$ Bottom

1. Binary to Decimal Conversion (Including Fractions)

A. Converting Binary Integers to Decimal

Rule: For the integer part (left of the binary point), positional values increase from right to left as powers of 2 ($2^0, 2^1, 2^2, 2^3, 2^4, 2^5, 2^6...$).
This corresponds to the values: 1, 2, 4, 8, 16, 32, 64, etc.

B. Converting Binary Fractions to Decimal

Rule: For the fractional part (right of the binary point), positional values decrease from left to right as negative powers of 2 ($2^{-1}, 2^{-2}, 2^{-3}...$).
This corresponds to the decimal values: 0.5, 0.25, 0.125, 0.0625, etc.
Example Calculation: Convert $(1001101.01101)_2$ to Decimal.
- Integer Part $(1001101)_2$: $(1 \times 64) + (0 \times 32) + (0 \times 16) + (1 \times 8) + (1 \times 4) + (0 \times 2) + (1 \times 1) = \mathbf{77}$.
- Fractional Part $(.01101)_2$: $(0 \times 0.5) + (1 \times 0.25) + (1 \times 0.125) + (0 \times 0.0625) + (1 \times 0.03125) = \mathbf{0.40625}$.
- Final Answer: $(77.40625)_{10}$.

2. Binary to Octal Conversion

Key Concept: The base of Binary is 2 and Octal is 8. Since $8 = 2^3$, exactly three binary bits represent one octal digit.

Rules for Grouping Bits:

For Integers: Start from the right side and group bits into sets of three moving left. If the last group falls short, add leading zeros to the left.
For Fractions: Start from the left side (immediately after the binary point) and group bits into sets of three moving right. If the last group falls short, add trailing zeros to the right.
Conversion: Replace each 3-bit group with its corresponding Octal equivalent.

Example: $(1110111001.1000011)_2$ becomes $(001 \ 110 \ 111 \ 001 \ . \ 100 \ 001 \ 100)_2$ = $(1671.414)_8$.

3. Binary to Hexadecimal Conversion

Key Concept: The base of Hexadecimal is 16. Since $16 = 2^4$, exactly four binary bits represent one hexadecimal digit.

Rules for Grouping Bits:

For Integers: Start from the right side and group bits into sets of four moving left. Add leading zeros to the left if needed.
For Fractions: Start from the left side (after the binary point) and group bits into sets of four moving right. Add trailing zeros to the right if needed.
Conversion: Replace each 4-bit group with its Hexadecimal equivalent.

Example: $(110011011101.10110011)_2$ groups directly into 4s: $(1100 \ 1101 \ 1101 \ . \ 1011 \ 0011)2$. This translates to $(C \ D \ D \ . \ B \ 3)$ = **$(CDD.B3){16}$**.

(Note: An alternative method is to first convert the binary number into a decimal number, and then convert that decimal number into octal or hexadecimal).

4. Octal to Decimal Conversion (Introduction)

Concept: Converting an Octal integer to Decimal follows the exact same logic as Binary to Decimal. However, instead of multiplying by powers of 2, you multiply the digits by increasing powers of 8 (from right to left).

5. Quick Revision Tables

Table 1: 3-Bit Binary to Octal Reference

Octal Digit	Binary Equivalent (3-bit)
0	000
1	001
2	010
3	011
4	100
5	101
6	110
7	111

Table 2: 4-Bit Binary to Hexadecimal Reference

Hexadecimal Digit	Binary (4-bit)	Hexadecimal Digit	Binary (4-bit)
0	0000	8	1000
1	0001	9	1001
2	0010	A (10)	1010
3	0011	B (11)	1011
4	0100	C (12)	1100
5	0101	D (13)	1101
6	0110	E (14)	1110
7	0111	F (15)	1111

1. Binary to Decimal Conversion (Including Fractions)

Key Concept: Converting binary numbers to decimal requires multiplying each bit by its positional value and summing the results,.
Integer Positional Values: Moving from right to left (before the binary point), positional values increase in positive powers of 2 ($2^0, 2^1, 2^2, 2^3, 2^4, 2^5, 2^6$, etc.), which corresponds to 1, 2, 4, 8, 16, 32, 64.
Fractional Positional Values: Moving from left to right (after the binary point), positional values decrease in negative powers of 2 ($2^{-1}, 2^{-2}, 2^{-3}$, etc.), which corresponds to decimal values of 0.5, 0.25, 0.125, 0.0625,.

Example: Convert $(1001101.01101)_2$ to Decimal

Step 1: Integer Part $(1001101)_2$
- Calculation: $(1 \times 64) + (0 \times 32) + (0 \times 16) + (1 \times 8) + (1 \times 4) + (0 \times 2) + (1 \times 1)$,.
- Result: $77$.
Step 2: Fractional Part $(.01101)_2$
- Calculation: $(0 \times 0.5) + (1 \times 0.25) + (1 \times 0.125) + (0 \times 0.0625) + (1 \times 0.03125)$.
- Result: $0.40625$.
Final Answer: Combining both parts gives $(77.40625)_{10}$.

2. Binary to Octal Conversion

The Power Rule: The base of Binary is 2 and the base of Octal is 8. Since $8 = 2^3$, every single octal digit can be represented by exactly three binary bits.

Rules for Grouping Bits:

For Integers (Whole Numbers): Start from the right side and create groups of 3 bits moving left. If the leftmost group is incomplete, add leading zero(s) to finish the 3-bit group. Finally, substitute each group with its Octal value.
For Fractions: Start from the left side (immediately after the binary point) and create groups of 3 bits moving right. If the rightmost group is incomplete, add trailing zero(s) to finish it. Substitute each group with its Octal value.

Example: Convert $(1110111001.1000011)_2$ to Octal

Grouping: $001 \ 110 \ 111 \ 001 \ . \ 100 \ 001 \ 100$. (Notice the added padding zeros on the extreme left and extreme right),.
Translation: $1 \ \ 6 \ \ 7 \ \ 1 \ . \ 4 \ \ 1 \ \ 4$.
Final Answer: $(1671.414)_8$.

3. Binary to Hexadecimal Conversion

The Power Rule: The base of Binary is 2 and the base of Hexadecimal is 16. Since $16 = 2^4$, every single hexadecimal digit can be represented by exactly four binary bits.

Rules for Grouping Bits:

For Integers: Start from the right side and create groups of 4 bits moving left. Add leading zero(s) if necessary to complete the final group,. Substitute with the corresponding Hexadecimal value.
For Fractions: Start from the left side (after the binary point) and create groups of 4 bits moving right,. Add trailing zero(s) if necessary to complete the final group. Substitute with the corresponding Hexadecimal value.

Example: Convert $(110011011101.10110011)_2$ to Hexadecimal

Grouping: $1100 \ 1101 \ 1101 \ . \ 1011 \ 0011$.
Translation: $C \ \ \ \ D \ \ \ \ D \ \ \ . \ \ \ B \ \ \ \ 3$.
Final Answer: $(CDD.B3)_{16}$.
Note on Alternative Method: Instead of direct grouping, a binary number can also be converted into a decimal number first, and then converted from decimal into hexadecimal (or octal),.

4. Octal to Decimal Conversion (Introduction)

Key Concept: Converting an Octal integer to a Decimal integer uses the exact same method as converting a Binary integer to Decimal.
The Difference: Instead of multiplying bits by powers of 2, the octal digits are multiplied by increasing powers of 8 (moving from right to left),.

5. Quick Revision Reference Tables

Table 1: 3-Bit Binary to Octal Translation

Octal Digit	Binary Equivalent (3-bit)
0	000
1	001
2	010
3	011
4	100
5	101
6	110
7	111

Table 2: 4-Bit Binary to Hexadecimal Translation

Hexadecimal Digit	Binary (4-bit)	Hexadecimal Digit	Binary (4-bit)
0	0000	8	1000
1	0001	9	1001
2	0010	A	1010
3	0011	B	1011
4	0100	C	1100
5	0101	D	1101
6	0110	E	1110
7	0111	F	1111

Here are the continuation of your exam-oriented study notes, translated into English based on the newly provided document (Page 18).

Study Notes: Advanced Conversions and Computer Codes (Part 4)

1. Octal Number System Conversions

A. Octal to Decimal Conversion (Including Fractions)

Rule for Integers: Multiply each digit by increasing positive powers of 8 (e.g., $8^0, 8^1, 8^2$) moving from right to left.
Rule for Fractions: Multiply each digit by increasing negative powers of 8 (e.g., $8^{-1}, 8^{-2}, 8^{-3}$) moving from left to right.
Example Calculation: Convert $(427.235)_8$ to Decimal.
- Integer Part $(427)_8$: $(4 \times 64) + (2 \times 8) + (7 \times 1) = \mathbf{279}$.
- Fractional Part $(.235)_8$: $(2 \times 0.125) + (3 \times 0.015625) + (5 \times 0.0019531) = \mathbf{0.306640}$.
- Final Answer: $(279.306640)_{10}$ (approximate).

B. Octal to Binary Conversion

Key Concept: This is extremely simple. Replace each single Octal digit with its exact 3-bit binary equivalent.
Example: Convert $(325.614)_8$ to Binary.
- $3 = 011$ | $2 = 010$ | $5 = 101$ | . | $6 = 110$ | $1 = 001$ | $4 = 100$.
- Final Answer: $(011010101.110001100)_2$.

C. Octal to Hexadecimal Conversion

Step-by-Step Method:
1. First, convert the Octal number into a Binary number (using 3-bit groups).
2. Next, regroup that newly formed Binary number into sets of 4 bits and convert it into Hexadecimal.
Example: Convert $(7632)_8$ to Hexadecimal.
- Octal to Binary: $7(111) \ 6(110) \ 3(011) \ 2(010) \rightarrow (111110011010)_2$.
- Binary to Hex (Group in 4s): $1111(F) \ 1001(9) \ 1010(A)$.
- Final Answer: $(F9A)_{16}$.
Alternative Method: You can also convert the Octal number to Decimal first, and then convert that Decimal number to Hexadecimal.

2. Hexadecimal Number System Conversions

A. Hexadecimal to Decimal Conversion

Rule: Multiply each digit by increasing positive powers of 16 ($16^0, 16^1, 16^2$) moving right to left.
Example: Convert $(1B4)_{16}$ to Decimal.
- $(1 \times 256) + (11 \times 16) + (4 \times 1) = 256 + 176 + 4 = \mathbf{436}$.
- Final Answer: $(436)_{10}$.

B. Hexadecimal to Binary Conversion

Key Concept: Extremely simple. Replace each single Hexadecimal digit with its exact 4-bit binary equivalent.
Example: Convert $(D7A)_{16}$ to Binary.
- $D(1101) \ 7(0111) \ A(1010)$.
- Final Answer: $(110101111010)_2$.

C. Hexadecimal to Octal Conversion

Step-by-Step Method:
1. Convert the Hexadecimal number to Binary (using 4-bit groups).
2. Regroup that Binary number into sets of 3 bits to convert it into Octal.
Example: Convert $(AC2D)_{16}$ to Octal.
- Hex to Binary: $A(1010) \ C(1100) \ 2(0010) \ D(1101)$.
- Binary to Octal (Group in 3s from right): $001(1) \ 010(2) \ 110(6) \ 000(0) \ 101(5) \ 101(5)$.
- Final Answer: $(126055)_8$.

3. Computer Codes

Definition: Computers need a specific binary-based code to represent, store, and process characters (alphabets, numbers, or symbols). These are called Computer Codes.

I. BCD (Binary Coded Decimal)

Mechanism: Uses a 4-bit group to represent every single decimal digit (0 through 9).
Size Limit: There is no size limit in the BCD system. No matter how large the number is, each digit is independently converted into a 4-bit group.
Example: $143924 = 0001 \ 0100 \ 0011 \ 1001 \ 0010 \ 0100$.

II. ASCII (American Standard Code for Information Interchange)

Usage: A standard character code used by programs to store and utilize data.
Two Types:
1. ASCII-7: A 7-bit standard code that can represent a total of 128 ($2^7$) characters.
2. ASCII-8: An upgraded 8-bit version that can represent 256 ($2^8$) characters.

III. EBCDIC (Extended Binary Coded Decimal Interchange Code)

Mechanism: Groups characters into 8 bits.
Usage: Used to store information on any type of computer.
Capacity: Represents up to 256 ($2^8$) characters.

4. Quick Revision Tables

Table 1: Computer Codes Comparison

Code Name	Full Form	Bit Size	Total Characters Represented	Key Feature
BCD	Binary Coded Decimal	4-bit (per digit)	0-9 (Numeric only)	No size limit for the total number. Developed by IBM.
ASCII-7	American Standard Code for Information Interchange	7-bit	128 ($2^7$)	Standard basic code for data storage.
ASCII-8	(Same as above)	8-bit	256 ($2^8$)	Upgraded version of ASCII-7.
EBCDIC	Extended Binary Coded Decimal Interchange Code	8-bit	256 ($2^8$)	Universal character representation.
UNICODE	(Not explicitly expanded in text)	16-bit	Massive	Supports English, Scientific symbols, Chinese, Japanese, etc..

Summary & Revision Notes

Important Takeaway Points for Quick Revision:

Data Representation is simply the translation of real-world inputs (letters/audio/video) into computer-readable formats (0s and 1s).
Computers only understand Binary Language (Base 2) internally, acting as electronic switches where 0 = OFF and 1 = ON.
A number's base dictates its multipliers; moving right-to-left from the decimal/binary/octal point scales positional value by the power of the base (e.g., $10^0, 10^1...$ or $2^0, 2^1...$).
Notation matters: Always indicate the number system by placing the base as a subscript outside parentheses (e.g., $(25){10}$ or $(1A){16}$).
Hexadecimal Trap: Remember that 10 through 15 are replaced by A through F so the computer doesn't mistake a two-digit number for two separate single digits.

Dividing vs. Multiplying: When converting out of Decimal, always Divide the whole numbers and Multiply the fractions.
The Magic Numbers (Bases): Use 2 for Binary, 8 for Octal, and 16 for Hexadecimal as your divisor/multiplier.
Direction is crucial:
- For integers (division), write the remainders from bottom to top.
- For fractions (multiplication), write the resulting whole numbers from top to bottom.
Hexadecimal Alert: Do not forget to convert remainders of 10-15 into letters (A-F) when dividing by 16 (e.g., a remainder of 15 becomes F, 11 becomes B).

Binary Fractions to Decimal: Remember to multiply fractional bits by $0.5, 0.25, 0.125$, etc., moving left to right.
The Power Rule for Grouping: Since $8 = 2^\mathbf{3}$, Octal uses 3-bit groupings. Since $16 = 2^\mathbf{4}$, Hexadecimal uses 4-bit groupings.
Padding Rule (Crucial for Exams):
- For Integers, add padding zeros to the far Left.
- For Fractions, add padding zeros to the far Right.
Direct Conversion: You can instantly jump between Binary and Octal/Hex without going through Decimal if you memorize the 3-bit and 4-bit grouping tables.

Positional Math: Binary fractions use negative powers of 2 ($0.5, 0.25, 0.125$) while integers use positive powers ($1, 2, 4, 8$),.
The "Magic Groupings":
- Octal Conversion = Group into 3 bits (because $2^3 = 8$).
- Hexadecimal Conversion = Group into 4 bits (because $2^4 = 16$).
Crucial Padding Rule: When forming groups, add extra zeros to the extreme left for integers, and to the extreme right for fractions,,,.
Octal to Decimal Logic: The logic remains identical to binary-to-decimal, but the multiplier base changes from 2 to 8,.

IBM's Creation: The BCD (Binary Coded Decimal) system was developed by the IBM Corporation.
Universal Language (UNICODE): UNICODE uses 16 bits to represent symbols. It can handle complex languages (like Chinese and Japanese) and scientific symbols along with English alphabets.
The Sign Bit (MSB):
- Used to indicate if a number is Positive (+) or Negative (-).
- It is always the Most Significant Bit (MSB), meaning it is the very first bit on the left in binary representation.
- 0 = Positive Number.
- 1 = Negative Number.

Bridging Base 8 and Base 16: To jump between Octal and Hexadecimal, always use Binary as your middle bridge. (Octal $\rightarrow$ 3-bit Binary $\rightarrow$ Regroup to 4-bit $\rightarrow$ Hex) or vice versa.
Code Capacities: Memorize the bits! BCD is 4-bit per digit, ASCII-7 is 7-bit (128 chars), ASCII-8 and EBCDIC are 8-bit (256 chars), and UNICODE is 16-bit.
MSB / Sign Bit Rule: The far-left bit dictates the sign. $0 = (+)$ and $1 = (-)$.

Numeric