Binary number system exam tips

Exam tips

• Check the number of bits first

  Before converting or finding a range, write down the place values for the exact number of bits stated.

  The place values and the maximum possible value depend directly on the bit length; using the wrong length changes the answer.

• Align before calculating

  Write binary values in columns with matching place values aligned, and add leading zeroes where needed.

  Correct alignment makes carries and multiplication shifts easier to track and reduces place-value errors.

• Write the bit width first

  Keep the required number of bits visible throughout every conversion and calculation, and discard only a carry beyond that width.

  Two’s complement values and their ranges depend on the fixed number of bits; changing the width can change the represented value.

• Record the format before converting

  Identify the number of bits, the position of the fixed-point binary point, and the floating-point convention before starting the calculation.

  The same bit pattern can represent different values if the binary-point position or mantissa convention changes.

• Link the explanation to binary fractions

  When explaining rounding errors, state whether the value can be represented exactly as a binary fraction in the available number of bits.

  This directly addresses the specification requirement and explains why the stored value may be an approximation.

• Show both stages of the calculation

  First calculate the absolute error, then use it to calculate the relative error. State clearly whether the final relative error is a decimal or a percentage.

  This makes the method clear and helps avoid confusing the difference between the two types of error.

• Compare all three factors

  When asked to compare fixed point and floating point, discuss range, precision and speed of calculation.

  These are the three explicit comparison criteria in the specification requirement, so omitting one leaves the comparison incomplete.

• Count every binary-point movement

  Count the number of places the binary point moves, then apply the same number to the exponent in the opposite direction.

  This provides a reliable method for preserving the value and avoids errors with positive and negative exponents.

• Link the condition to the range

  State that the representation has a fixed number of bits, identify its minimum and maximum values, and then say whether the result is above or below that range.

  This directly addresses both the cause and the circumstance of overflow or underflow, rather than merely naming the condition.