Floating Point Arithmetic

When adding floating point numbers, what is the primary concern regarding exponents?

• They should be kept as they are.
• They should be changed to different values.
• They should be ignored.
• They should match.

What is the final step in adding floating point numbers?

• Separate the mantissas.
• Check whether the numbers are normalised.
• Ensure the value is normalised.
• Add the exponents.

When subtracting one positive floating point number from another, what value is the second number converted into?

• Decimal value.
• Fraction.
• Two’s complement negative value.
• Positive value.

The following normalised floating point numbers are held in a 6 bit mantissa and a 4 bit exponent. Please show the result of 0101000010 + 0110100011. The result should be held in the original format.

Using floating point representation with 4 bits for the exponent and 4 bits for the mantissa, add together the following floating point binary numbers and write the answer as a normalised floating point number with 4 bits mantissa and 4 bit exponent.

0110 0010 and 0100 0011

The binary number R is not normalised. Write the normalised form of R. 8 bit Mantissa and 4 bit Exponent.

You must show your working.

R = 000110100101

Two floating point numbers are shown below. Calculate the answer of the second number subtracted from the first. You must show your working and ensure your answer is normalised.

01001100 0011 - 01001010 0010

Demonstrate subtraction on the two numbers below, both stored in normalised floating point format, using 6 bits for their mantissa and 4 for their exponent. Show the result in the same format. Show your working.

010010 0100 - 010010 0010

Add together the two numbers below. Both numbers are stored in normalised floating point format, using 6 bits for their mantissa and 4 bits for their exponent which are both in two’s complement. Show the result in the same format and show your working.

 0110000110    + 0101000100

Table 3 here shows floating point numbers that are stored using 6 bits for the mantissa and 3 bits for the exponent, both in two’s complement.

Tick (✓) one box in each row to state whether each number is normalised or not normalised.