Topic Details (Notes format)

How to Convert Between Different Number Bases

Subject: Mathematics

Book: Maths Mastery

Number systems like binary (base 2), octal (base 8), and hexadecimal (base 16) appear in computing, while decimal is base 10. To convert a decimal integer to binary, repeatedly divide by 2, gathering remainders. For example, 13 in binary is 1101. Reversely, sum place values 1×2³+1×2²+0×2¹+1×2⁰=8+4+0+1=13. Conversions among bases are vital in digital electronics, programming (memory addresses), or cryptographic systems. Mastering them fosters agility with computational tasks and fosters deeper understanding of how digital systems store and process numbers.

Practice Questions

The sum of the reciprocals of two numbers is 1/4. If one number is 12, what is the other?

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The area of an equilateral triangle with side length 6 cm is:

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If sin(A) = 1/2 and A is acute, what is the value of A?

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If 8x = 512, what is the value of x?

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If a+b = 10 and ab = 21, what is the value of a^3 + b^3?

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If 2x = 16, what is the value of x?

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A rectangle has a length of 10 cm and a width of 5 cm. What is the diagonal of the rectangle?

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What is the length of the diagonal of a square with a side length of 7 cm?

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If 3x = 81, what is the value of x?

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If log(100) = 2 and log(10) = 1, what is log(1000)?

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