What is the defining characteristic of the decimal number system?

The decimal system is a base 10 system, meaning it uses ten distinct digits, 0 through 9.

What two numbers are used exclusively in the binary system?

The binary system uses only two numbers: 0, which typically means 'off', and 1, which means the system is in the 'on' state.

How is the hexadecimal system base derived?

The hexadecimal system is a base 16 system, derived from combining 'hexa' (six) and 'decimal' (ten), summing up to 16.

What is the method used to convert a decimal number to binary, octal, or hexadecimal?

The conversion method demonstrated is successive division, where the decimal number is repeatedly divided by the target base (2, 8, or 16), and the remainders are collected.

When converting 348 base 10 to hexadecimal, what does a remainder of 12 correspond to in the final result?

A remainder of 12 in the hexadecimal conversion corresponds to the letter 'C'.

Number Systems Introduction - Decimal, Binary, Octal & Hexadecimal

Number Systems Overview
📌 The Decimal System is a base 10 system using digits 0 through 9, commonly used for everyday counting.
💻 The Binary System is a base 2 system using only 0 (off) and 1 (on), essential for computers and digital circuits.
🔢 The Octal System is a base 8 system using digits 0 through 7, derived from the prefix 'octa' meaning eight.
🔠 The Hexadecimal System is a base 16 system using digits 0-9 and letters A-F, where A=10, B=11, C=12, D=13, E=14, and F=15.

Decimal to Other Bases Conversion (Successive Division)
➡️ To convert a decimal number (e.g., $348_{10}$ ) to Binary (Base 2), repeatedly divide by 2 and record the remainders, reading the result from the bottom (Most Significant Bit) up.
➡️ To convert to Octal (Base 8), use the same successive division technique but divide by 8 each time, reading the remainders bottom-up (e.g., $348_{10} = 534_8$ ).
➡️ To convert to Hexadecimal (Base 16), repeatedly divide by 16, converting any remainder greater than 9 to its corresponding letter (e.g., $348_{10} = 15C_{16}$ , where 12 is C).

Key Points & Insights
➡️ Understanding number system bases (10, 2, 8, 16) is foundational for working with digital systems and computation.
➡️ The successive division method is the standard technique for converting from decimal to lower bases by tracking the remainders.
➡️ Remember that in base conversion, the remainders must be read in reverse order (bottom to top) to obtain the correct representation in the new base.
➡️ Hexadecimal representation requires mapping decimal values 10 through 15 to the letters A through F.

📸 Video summarized with SummaryTube.com on Oct 09, 2025, 01:03 UTC

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Number Systems Introduction - Decimal, Binary, Octal & Hexadecimal

AI Summary of "Number Systems Introduction - Decimal, Binary, Octal & Hexadecimal"

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