Floating-Point Binary to Decimal 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?
I got the answer with a bit of reverse engineering.

1) 0111 is 7 in denary so the exponent is power(2,7)

2) convert 10101000 to a positive number using twos comp

3) you  you get: 010110000 which is 1/2 + 1/ 8 + 1/16 using the powers of 2 after the radix point

4) this is 11/16 but we no it is negative from step 2 so it is -11/16!