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Number Systems For Computer Scientists

Floating Point Representation

Learn how floating point representation extends fixed point notation to encode fractional numbers in binary. Understand the roles of the sign bit, biased exponent, and mantissa in storing numbers with fractional parts using an 8-bit binary format.

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How does it work?

Just like scientific notation is an extension of the decimal point notation, floating points can be said to extend fixed point notation.

Let’s look at a number in scientific notation:

ss m×10nm \times 10^{n}

We can divide this number into three distinct parts:

  • The coefficient mm, known as the significand or the mantissa, which can be any real number
  • The power of 1010, nn, which is called the exponent, and
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