Guided Floating Point Binary Conversion questions

This macro-enabled spreadsheet is designed to practice converting from Decimal to Floating Point Binary as used in Computing, and vice-versa.

There are two worksheets, one with questions converting from Decimal to Floating Point Binary, and one with questions converting from Floating Point Binary to Decimal.

Learners are guided through the steps necessary to complete each type of question, namely:

## Decimal to Floating Point Binary

- Calculating the positive signed raw Binary;
- Twos Complementing to obtain the negative raw Binary, if required;
- Determining the distance the point floats;
- Determining the direction the point floats;
- Determining the positive Decimal value of the Exponent;
- Calculating the Binary value of the Exponent;
- Twos Complementing to obtain the negative Binary value of the Exponent if required;
- Working out the Mantissa;
- Giving the full Floating Point Binary.

## Floating Point Binary to Decimal

- Calculating the positive signed raw Binary;
- Working out the Mantissa;
- Working out the Binary Exponent;
- Twos Complementing to obtain the positive Binary value of the Exponent to determine its magnitude if required;
- Determining the Decimal value of the Exponent;
- Determining the distance the point floats;
- Determining the direction the point floats;
- Un-normalising the Binary Mantissa into its raw Floating Point form;
- Twos Complementing to obtain the positive Binary value of the raw Floating Point Binary Mantissa to determine its magnitude if required;
- Giving the Decimal value.

The size of the Mantissa can be varied between 4 and 8 bits in size, and 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 sizes of the Mantissa and Exponent affect the range of values which can be stored and the accuracy with which they can be represented.

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 which steps of their answer are right or wrong. Changing an answer removes the marking until the button is clicked again.

This worksheet is designed to be used prior to completing our ‘Unguided Floating Point Binary questions’ worksheet.

NOTE: for this spreadsheet to work correctly, the copy of Excel in which it is running must allow macros to execute, and ‘Enable Content’ must be clicked when the spreadsheet is opened.