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Binary to Decimal Conversion:
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Binary to Decimal Conversion

How is binary used in computer architecture?

Binary is fundamental to computer architecture because it directly aligns with how electronic circuits work, using two discrete states: 0 (off/low) and 1 (on/high). Here's how binary is applied in different aspects of computer architecture:

⋆ 1. Data Representation : All forms of data—whether text, numbers, images, or audio—are stored and processed as binary in computers.



Text: Represented using binary encodings like ASCII or Unicode (e.g., the letter "A" is 01000001 in binary).

Uppercase Letters (A-Z):

'A': ASCII = Decimal 65 to Binary 01000001 to Hexadecimal = 0x41

'B': ASCII = Decimal 66 to Binary 01000010 to Hexadecimal = 0x42

'C': ASCII = Decimal 67 to Binary 01000011 to Hexadecimal = 0x43

'D': ASCII = Decimal 68 to Binary 01000100 to Hexadecimal = 0x44

'E': ASCII = Decimal 69 to Hexadecimal = 0x45



'F': ASCII = Decimal 70 to Hexadecimal = 0x46

'G': ASCII = Decimal 71 to Hexadecimal = 0x47

'H': ASCII = Decimal 72 to Hexadecimal = 0x48

'I': ASCII = Decimal 73 to Hexadecimal = 0x49

'J': ASCII = Decimal 74 to Hexadecimal = 0x4A

'K': ASCII = Decimal 75 to Hexadecimal = 0x4B



'L': ASCII = Decimal 76 to Hexadecimal = 0x4C

'M': ASCII = Decimal 77 to Hexadecimal = 0x4D

'N': ASCII = Decimal 78 to Hexadecimal = 0x4E

'O': ASCII = Decimal 79 to Hexadecimal = 0x4F

'P': ASCII = Decimal 80 to Hexadecimal = 0x50

'Q': ASCII = Decimal 81 to Hexadecimal = 0x51



'R': ASCII = Decimal 82 to Hexadecimal = 0x52

'S': ASCII = Decimal 83 to Hexadecimal = 0x53

'T': ASCII = Decimal 84 to Hexadecimal = 0x54

'U': ASCII = Decimal 85 to Hexadecimal = 0x55

'V': ASCII = Decimal 86 to Hexadecimal = 0x56

'W': ASCII = Decimal 87 to Hexadecimal = 0x57



'X': ASCII = Decimal 88 to Hexadecimal = 0x58

'Y': ASCII = Decimal 89 to Hexadecimal = 0x59

'Z': ASCII = Decimal 90 to Hexadecimal = 0x5A

Lowercase Letters (a-z):

'a': ASCII = Decimal 97 to Hexadecimal = 0x61

'b': ASCII = Decimal 98 to Hexadecimal = 0x62

'c': ASCII = Decimal 99 to Hexadecimal = 0x63

'd': ASCII = Decimal 100 to Hexadecimal = 0x64

'e': ASCII = Decimal 101 to Hexadecimal = 0x65



'f': ASCII = Decimal 102 to Hexadecimal = 0x66

'g': ASCII = Decimal 103 to Hexadecimal = 0x67

'h': ASCII = Decimal 104 to Hexadecimal = 0x68

'i': ASCII = Decimal 105 to Hexadecimal = 0x69

'j': ASCII = Decimal 106 to Hexadecimal = 0x6A

'k': ASCII = Decimal 107 to Hexadecimal = 0x6B



'l': ASCII = Decimal 108 to Hexadecimal = 0x6C

'm': ASCII = Decimal 109 to Hexadecimal = 0x6D

'n': ASCII = Decimal 110 to Hexadecimal = 0x6E

'o': ASCII = Decimal 111 to Hexadecimal = 0x6F

'p': ASCII = Decimal 112 to Hexadecimal = 0x70

'q': ASCII = Decimal 113 to Hexadecimal = 0x71



'r': ASCII = Decimal 114 to Hexadecimal = 0x72

's': ASCII = Decimal 115 to Hexadecimal = 0x73

't': ASCII = Decimal 116 to Hexadecimal = 0x74

'u': ASCII = Decimal 117 to Hexadecimal = 0x75

'v': ASCII = Decimal 118 to Hexadecimal = 0x76

'w': ASCII = Decimal 119 to Hexadecimal = 0x77



'x': ASCII = Decimal 120 to Hexadecimal = 0x78

'y': ASCII = Decimal 121 to Hexadecimal = 0x79

'z': ASCII = Decimal 122 to Hexadecimal = 0x7A



Numbers: Represented in binary numeral systems (e.g., decimal 5 is 101 in binary).

Images and Media: Translated into binary sequences to store color values (e.g., RGB) or sound waves.

⋆ 2. Boolean Logic : Binary forms the basis for all logic operations in a computer. Logic gates, such as AND, OR, NOT, and XOR, operate on binary inputs to perform fundamental calculations and comparisons.



⋆ 3. Processor Operation : The Central Processing Unit (CPU) executes instructions encoded as binary machine code. For example:

A binary instruction like 10110000 might instruct the CPU to load a value into a register.

These instructions are decoded, processed, and executed to perform tasks.

all CPUs, GPUs, and TPUs execute instructions using binary code. That’s the universal language of digital hardware.

Binary (0s and 1s) aligns perfectly with the physical nature of electronic circuits: 0 = low voltage (off) ; 1 = high voltage (on)

ARM Architecture Reference Manual

Intel 64 AND IA-32 Architecture Reference Manual

NVIDIA PTX ISA Architecture Reference Manual

These states are controlled by billions of transistors inside chips, which act as tiny switches. So whether it's a CPU calculating your spreadsheet, a GPU rendering a game, or a TPU training a neural network—they're all flipping switches based on binary instructions.

Executes machine code instructions encoded in binary. These instructions are fetched from memory, decoded, and executed by the control unit and ALU (Arithmetic Logic Unit). Instruction sets like x86 or ARM define how binary sequences map to operations like ADD, MOV, or JMP.

Stanford Computer Science 101 explains how human-readable code is compiled into binary machine instructions that CPUs understand.

GPU (Graphics Processing Unit) Also runs binary machine instructions, but optimized for parallel processing.Uses instruction sets like PTX (NVIDIA) or GCN (AMD), which are compiled down to binary for execution. Each thread or shader core executes binary instructions simultaneously across many data points.

MIT OpenCourseWare - Computer Operating System Offers free lectures and notes on binary encoding and processor design.



⋆ 4. Memory and Storage : Memory is organized into bits (binary digits) and bytes (8 bits). Each memory cell stores binary values (0 or 1).

Binary addressing allows the CPU to locate and retrieve data from memory.

⋆ 5. Arithmetic and Logical Operations : Binary arithmetic is central to computer architecture. Addition, Subtraction, Multiplication, Division: Performed using binary algorithms.

Processors implement circuits like adders (e.g., half-adder, full-adder) to perform binary addition.



⋆ 6. Digital Communication : Bus Systems: Binary signals travel along buses in the computer to transfer data between components like the CPU, memory, and peripherals.

Networking: Binary is used to encode data for transmission over networks.

⋆ 7. Instruction Set Architecture (ISA) : The instruction set of a processor is based on binary codes that define operations. For example:

0001: Add two registers.

0010: Subtract one register from another.



⋆ 8. Error Detection and Correction : Binary systems employ methods like parity bits or error-correcting codes (e.g., Hamming code) to identify and fix errors in data transmission or storage.

⋆ 9. Control Signals: Binary control signals are used to manage operations in a computer, such as enabling/disabling specific hardware components or switching between operations.

⋆ 10. Binary Logic in Hardware Design: All digital circuits, such as those in CPUs and GPUs, use transistors that switch between binary states to perform computations.

How is binary represented in electronic circuits?

Binary is represented in electronic circuits using two voltage levels, which correspond to the two binary digits: 0 and 1. These are the foundation of digital electronics and computing. Here’s how it works:

⋆ 1. Voltage Levels for Binary: Binary 1 (High): Represented by a higher voltage level. For example, in many circuits, this might be 5V or 3.3V.



⋆ 2. Logic Gates: Logic gates are the building blocks of binary operations in electronic circuits:

These gates process binary signals and perform computations

AND Gate: Produces a binary 1 only if all inputs are 1.

OR Gate: Produces a binary 1 if at least one input is 1.

NOT Gate: Inverts the input; 0 becomes 1, and 1 becomes 0.



⋆ 3. Transistor as Switches Transistors are used to build logic gates and process binary data.

By combining transistors in specific arrangements, logic gates are formed, and binary computations are executed.

In transistor: ON State (Closed): Current flows, representing binary 1.

OFF State (Open): No current flows, representing binary 0.



⋆ 4. Flip-Flops and Memory Storage Binary values are also stored in circuits using devices called flip-flops, which are composed of multiple transistors.

A flip-flop can hold a binary 0 or 1 until it is reset or updated, enabling the storage of data in computer memory.

⋆ 5. Communication in Binary Binary signals are transmitted through wires or circuits or over the air, with voltage pulses or digital signals representing sequences of 0s and 1s.

In modern computing, the entire architecture—processors, memory, and storage—is based on binary representation.

How is binary knowledge associated with modern AI voice to text natural language processing?

⋆ 1. How did computer remember the word "apple"?

First the computer will look up at memory table for ASCII conversion for first letter 'a'. The ASCII equivalent number is 97 to binary 1100001 to hexadecimal 0x61

"apple" written in hexadecimal computer code and matrix format.

[0x61, 0x70, 0x70, 0x6C, 0x65]

"cat" written in ASCII decimal computer code [99, 97, 116, 0, 0 ] fixed-length vector is 5

When you convert the letter to ASCII decimal number, binary, or hexadecimal number the process is called embedding or transformation.



Every large language model have their own predefined vocabulary table for token ID mapping. Important things to remember, every word must be converted to decimal number, binary number or hexadecimal number.

Example "cat" will have predefined token id 1023 in decimal format
then "dog" will have predefned token id 1546 in decimal format
then "bat" will have predefined token id 982 in decimal format

These numbers are just examples. Every LLM providers might have their own predefined voabulary table.



What are other types of embeddings in NLP ?

In Natural Language Processing (NLP), embeddings are techniques used to represent textual data in numerical formats for machine learning models.

ASCII or Unicode embedding - very simple

TF-IDF (Term Frequency-Inverse Document Frequency): Useful for information retrieval, search engines, keyword extraction

BERT Embeddings: Contextual embeddings generated by transformer-based models like BERT (Bidirectional Encoder Representations from Transformers). These embeddings are contextualized at both token and sentence levels.



OpenAI's GPT Embeddings: Uses transformer-based embeddings for tasks like language generation and understanding. Often fine-tuned for specific tasks.

GPT - Generative Pre-Trained Transformer was observed to be very good in context but requires a lot of matrix multiplication to convert the word and its contextual meaning into decimal number or binary number or hexadecimal number. This embedding or number conversion is now possible because of GPU that can convert many words or tokens. The input context token for GPT-3 is up to 4,096 tokens. For GPT-4 up to 32,000+ tokens.



What type of database was used to store the embeddings in Llama 4, large language model?

Llama 4 embeddings are stored using vector databases , which are optimized for handling numerical representations of text. These databases enable efficient similarity searches and retrieval tasks.



Llama Index supports embedding models like OpenAI's text-embedding-ada-002 and Hugging Face embeddings, which can be used with vector databases



What is the average word count of 1 million token context window? How much is the cost of 1 million token context window?

The average word count of a 1 million-token context window depends on the language model's tokenization process. Tokens can represent words, subwords, or even characters, depending on the model. For example, OpenAI's models like GPT use a tokenizer that breaks text into subwords, meaning some words might split into multiple tokens (e.g., "running" could become "run" and "ning").

On average, for 1 million tokens, the word count would be approximately 750,000 words.

Calculate how many pages 750,000 words would fill on a standard 8.5x11-inch sheet of paper with single line spacing

The average word count per page with single line spacing is approximately 500 words. This depends on the font size (typically 12-point), margins (1 inch), and font type (like Times New Roman or Arial).

So, 750,000 words divided by 500 words per page equals 1,500 pages. This is an estimated number of pages.



What is MMLU benchmark ?

The MMLU benchmark stands for Massive Multitask Language Understanding. It is a widely used evaluation framework designed to test the capabilities of large language models across a diverse range of subjects.

Structure: MMLU consists of 15,908 multiple-choice questions spanning 57 subjects, including STEM fields, humanities, social sciences, and more

Purpose: It aims to assess a model's ability to perform well on tasks requiring specialized knowledge and reasoning, making it more challenging than simpler benchmarks

Performance: When first introduced, most models performed near random chance (~25%). Over time, advanced models like GPT-4 and Llama 3.1 have achieved scores close to human expert levels

Applications: MMLU is used to compare the generalization and reasoning capabilities of AI systems, helping researchers understand their strengths and limitations



What is GPQA benchmark ?

Graduate level Google Proof Q & A designed to evaluate AI systems on challenging academic questions

The diamond subset includes 198 questions that are particularly difficult. These questions were answered correctly by expert validators but stumped most non-experts, ensuring they require deep reasoning and understanding.



The questions span graduate-level topics in STEM fields like biology, physics, and chemistry, emphasizing areas where reasoning and specialized knowledge are critical.

The questions are crafted to be "Google-proof," meaning they cannot be easily answered by simple web searches. This ensures that AI systems rely on reasoning rather than fact recall.

Zero-shot chain-of-thought reasoning: Models solve problems while explaining their reasoning steps without prior examples.

Few-shot chain-of-thought reasoning: Models are provided with a few example questions and answers to guide their reasoning.

The diamond subset focuses on questions with unambiguous answers that challenge both AI systems and human experts. These questions are designed to test the limits of reasoning capabilities.

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How can IN-V-BAT-AI be used in classrooms ?

IN-V-BAT-AI is a valuable classroom tool that enhances both teaching and learning experiences. Here are some ways it can be utilized:

⋆ Personalized Learning : By storing and retrieving knowledge in the cloud, students can access tailored resources and revisit concepts they struggle with, ensuring a more individualized learning journey.

⋆ Memory Support : The tool helps students recall information even when stress or distractions hinder their memory, making it easier to retain and apply knowledge during homework assignments or projects.

⋆ Bridging Learning Gaps : It addresses learning loss by providing consistent access to educational materials, ensuring that students who miss lessons can catch up effectively.

⋆ Teacher Assistance : Educators can use the tool to provide targeted interventions to support learning.

⋆ Stress Reduction : By alleviating the pressure of memorization, students can focus on understanding and applying concepts, fostering a deeper engagement with the material.

🧠 IN-V-BAT-AI vs. Traditional EdTech: Why "Never Forget" Changes Everything

📚 While most EdTech platforms focus on delivering content or automating classrooms, IN-V-BAT-AI solves a deeper problem: forgetting.

✨Unlike adaptive learning systems that personalize what you learn, IN-V-BAT-AI personalizes what you remember. With over 504 pieces of instantly retrievable knowledge, it's your cloud-based memory assistant—built for exam prep, lifelong learning, and stress-free recall.

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"🧠 Forget less. Learn more. Remember on demand."
That's the IN-V-BAT-AI promise.

Personal Augmented Intelligence (AI) Explanation

🧠 Augmented Intelligence vs Artificial Intelligence

Understanding the difference between collaboration and automation

🔍 Messaging Contrast

Augmented Intelligence is like a co-pilot: it amplifies your strengths, helps you recall, analyze, and decide — but it never flies solo.

Artificial Intelligence is more like an autopilot: designed to take over the controls entirely, often without asking.

💡 Why It Matters for IN-V-BAT-AI

IN-V-BAT-AI is a textbook example of Augmented Intelligence. It empowers learners with one-click recall, traceable results, and emotionally resonant memory tools. Our “Never Forget” promise isn't about replacing human memory — it's about enhancing it.

Note: This is not real data — it is synthetic data generated using Co-Pilot to compare and contrast IN-V-BAT-AI with leading EdTech platforms.

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