Decoding
How to decode a binary floating-point number:
1. Analyse bit pattern according to the 3 field patterns (sign, exponent, mantissa)
2. Extract the mantissa and place the radix point on its left side. E.G., .1001
3. Extract the contents of the exponent field and interpret it using the Excess notation. (This 3-bit example is excess (4) notation so it represents 5-4 or +1.)
4. Move the radix the same number of positions as was determined from Step 3 above.
Move the radix right the number of bit position indicated by the exponent value if the exponent is positive value.
Move the radix left the number of bit position indicated by the exponent value (add 0's as necessary as placeholders) if exponent is negative value.
5. Using the original sign bit, represent the decoded number (in decimal.)
E.G. 01011001
Sign Exponent Mantissa
Bit in Excess(4) (Normalized)
The Sign bit is 0 so the number represented is a non-negative (+) number
Next, the number 101 in excess (4) notation is 5-4 that is +1; a positive exponent moves the radix to the right and a negative exponent moves the radix to the left.
The (normalized) mantissa 1001 is assumed to be .1001; after applying the exponent by moving the radix 1 position to the right, it becomes 1.001 or 1 and 1/8th.
Therefore the number 01011001 (in normalized floating point notation) represents the value +1 1/8.