I'm having difficulty with the following question:
Given a bit pattern with mantissa $10110000$ and exponent $0111$, what does the bit pattern represent in denary (i.e decimal / base 10)?
I got the right answer(!) but the wrong (or alternative) work:
- Convert the exponent to denary: $0111$ is $7$
- Apply this exponent to the mantissa: $10110000\rightarrow1011000$ after shifting $7$ places
- Convert the mantissa to denary: $1011000$ is $88$
- Set the sign: $-88$ (which is correct!)
Using a different method, the mantissa $1.0110000$ is somehow deteremined to be $-11/16$ and then $-11/16 \times 2^7 = - 88$ (I understand this shift with the exponent). However, what I don't understand is:
How do you convert 1.0101 (mantissa) to -11/16? Is this a standard way to do it?