Final answer:
The multiplication of two Tom's Tiny floating-point numbers requires multiplying the fractions, adding the exponents, and adjusting the final product to fit the 8-bit format with proper sign, exponent, and fraction.
Step-by-step explanation:
The multiplication of two Tom's Tiny 8-bit floating-point numbers A and B involves the following steps:
- Determine if the result will be positive or negative by looking at the sign bits. In this case, A is negative and B is negative, so the product will be positive.
- Add the exponents. Since these are in 2's complement form, we'll need to convert them to decimal, add them, and then convert back to 2's complement if necessary.
- Multiply the fractions.
- Normalize the result if necessary, so the fraction part is within the range for Tom's Tiny format.
- Round the fraction to fit the 4-bit limit, if necessary.
- Reassemble the sign, exponent, and fraction into the 8-bit format.
Application to A and B: A has a sign bit of 1 (negative), an exponent of 001 (2's complement for -3), and a fraction of 0011. B has a sign bit of 1 (negative), an exponent of 010 (2's complement for -2), and a fraction of 1000.
The product of A and B in Tom's Tiny format is a positive number (since both A and B are negative), with an exponent of -3 + (-2) = -5 (after converting to decimal), and a fraction part that is the product of the fractions. After normalizing and rounding, we have to fit this result back into the 8-bit format.