Endless Unguided Floating Point Binary Mathematics questions

This macro-enabled spreadsheet is designed to demonstrate the ability to add and subtract Floating Point Binary numbers as used in Computing.

There are two worksheets, one with addition, and one with subtraction.

The following options can be selected:

• The size of the Mantissa can be varied between 4 and 8 bits in size. This both changes the question difficulty and also gives learners an opportunity to appreciate how altering the size of the Mantissa affects the accuracy with which values can be represented.
• The size of the Exponent can be either 3 or 4 bits in size. This both changes the question difficulty and also gives learners an opportunity to appreciate how altering the size of the Exponent affects the range of values which can be stored.
• Both positive and negative Mantissae can be generated, or questions can be made simpler by allowing only positive Mantissae to be generated.
• There is an option to emulate how some processors treat the Carry Bit as an additional Sign Bit in certain conditions, allowing learners to determine the circumstances when this happens and the effect it has on eliminating Overflow.
With the Binary Exponent, both types of question use the convention with negative Binary numbers whereby if only the Sign Bit is a 1, it represents both sign and magnitude. For example, with a signed 4 bit Binary number, 1000 represents -8 in Decimal.

Each worksheet generates five questions every time the ‘Generate Questions’ button is clicked. Once the learners have completed a question, clicking the associated ‘Mark It’ button reveals whether their answer are right or wrong, and the steps required to complete the question successfully, namely:

• Converting the two values from Floating Point form to raw binary;
• Aligning the points of the raw binary values and padding out with additional Sign Bits and trailing zeroes as necessary;
• Twos Complementing the bottom of the point-aligned values (subtraction only);
• Performing the addition or subtraction of the point-aligned values;
• Determining the Mantissa, or if Overflow has occurred;
• Determining the Exponent, or if Overflow (the Exponent is a positive value too big to be represented in its selected number of bits) or Underflow (the Exponent is a negative value too big to be represented in its selected number of bits) has occurred;
• Giving the full Floating Point binary string if possible, or stating it is impossible to do so if not;
• Stating whether the Floating Point value has been truncated or not if it was possible to generate it.

Changing an answer removes the marking until the button is clicked again.

This worksheet is designed to be used after completing our ‘Guided Floating Point Binary questions’, ‘Unguided Floating Point Binary questions’ and ‘Guided Floating Point mathematics questions’ worksheets.