Converting Between Number Systems: A Comprehensive Lesson

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🔢 Example of converting numbers between number systems.

This video is about converting between number systems, specifically from base 10 to base 2, base 8, and base 16.

To understand this lesson, you need to be able to identify the base of a given number, state the symbol in the given base, and determine the quotient and remainder when dividing two numbers.

In the exercises, you will state the base of given numbers, identify the digits in base 16, and determine the quotient and remainder of operations.

🔢 Converting between number systems - decimal and base 16.

🔑 Understanding the base of a number and its representation.

➗ Dividing numbers and finding quotients and remainders.

Conversion from one base to another involves dividing the base 10 number by the target base and writing down the quotient and remainder.

The process is repeated until the quotient becomes zero, and the remainders are written down from the most recent to the least.

A common method to convert from base 10 to base 2 is introduced, which follows the same process but with a specific target base.

📊 Converting decimal numbers to binary can be done using a column diagram.

🔢 To convert, start from the right and raise 2 to the power of 0, then subtract each column heading from the decimal number.

⬇️ Repeat the process for each column until all columns have been calculated.

🔢 Converting between number systems involves using the tabular method and dividing the decimal number by the base.

💡 To convert from base 10 to base 2, we write a 1 if the heading of the column is less than or equals to the decimal number and subtract the heading from the decimal number.

🧮 In base 16, digits greater than or equal to 10 are replaced with letters: A = 10, B = 11, C = 12, D = 13, E = 14, F = 15.

💡 Converting from base 10 to base 2: divide the number by 2 and record the remainders.

💡 Converting from base 10 to base 8: divide the number by 8 and record the remainders.

💡 Converting from base 10 to base 16: use the tabular method to determine the values.