Floating-Point Multiplication 
1.0102×2-1 × –1.1102×2-2 = –1.0012×2-2
The following steps show how to multiply the above numbers in scientific notation. Again, we assume 4 bits of precision (or 3 bits of fraction).
Step 1. Calculating the Exponent of the Product 
   Product exponent (manual) = (–1) + (–2) = –3

   Product exponent (hardware)
 = EZ = EX + EY – Bias
 = (–1+127) + (–2+127) – 127
 = 124 (value = –3 = 124–127)
Step 2. Multiplying the Significands
Since sign SX≠SY, sign of product SZ=1 (negative). The result of multiplication is as follows: 
 1.0102×2-1 × –1.1102×2-2 = –10.0011002×2-3
Step 3. Normalizing the Product 
 –10.0011002×2-3 = –1.00011002×2-2
Shifting right by 1 bit has to be followed by incrementing the exponent. 
      1.010
  ×   1.110
 ————————————
       0000
      1010
     1010
  + 1010
 ———————————— 
   10001100 or

  10.001100
Step 4. Rounding the Significand
We assumed 4 bits of precision or 3 bits of fraction. Round the significand to nearest digit: –1.00011002×2-2 ≈ –1.0012×2-2

Step 5. Checking for Overflow or Underflow
Check whether exponent becomes too large (overflow) or too small (underflow).



      Q: What did the grape do when it got stepped on?    
      A: It let out a little wine!