Real numbers, truncation and rounding

Overview

Column values to the right of a binary point and limitation of a fixed point format.

What you need to know

Answer each one before you reveal it.

Questions from this subtopic

Each one with the model answer underneath.

1. 1

   What are the column values to the right of a binary point?

   Model answer

   They continue halving, so the columns are one half, one quarter, one eighth, one sixteenth and so on.

2. 2

   Convert 101.11 in binary to denary.

   Model answer

   The whole part is 4 + 1 = 5 and the fraction is one half plus one quarter, so the value is 5.75.

3. 3

   Convert 6.25 in denary to binary.

   Model answer

   The 6 gives 110 and the 0.25 gives .01, so the value is 110.01.

4. 4

   What is the limitation of a fixed point format?

   Model answer

   The binary point never moves, so the format must trade the size of the whole-number part against the precision of the fraction and cannot cover both very large and very small values.

5. 5

   What two parts make up a number held in floating point form?

   Model answer

   A mantissa holding the significant digits of the value, and an exponent recording how far the binary point must be moved.

6. 6

   What does the exponent do to the mantissa?

   Model answer

   It scales the mantissa by a power of two, shifting the binary point left or right, which is how a small number of bits can span an enormous range of magnitudes.

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