How does the excess-x representation for exponents of the scale factor int he fl

Question

How does the excess-x representation for exponents of the scale factor int he floating-point number representation of Figure 9.26a facilitate the comparison of the relative sizes of two floating-point numbers?

Some g .A signed scale factor exponent for an implied base of 2 bit represents the sign, S, for the number. The next 8 bits, E', represent the siehel signed of the scale factor (with an implied base of 2), and the remaini 32 bits Sign of8-bit signed 23-bit mantissa fraction exponent in 0 signifies + 1 signifies- representation E-127 Value represented-tl.M × 2 (a) Single precision 0 00101000001010 Value represented 1.00 1010 . . . 0 × 2-87 (b) Example of a single-precision number 64 bits 11-bit excess-1023 exponent 52-bit mantissa fraction Value represented E-1023 [. ±LM × 2 (c) Double precision Figure 9.26 IEEE standard floating-point formats

Explanation / Answer

The value of a IEEE-754 number is computed as:

Example :

If e = 00000001 or 00000000001 then 21-127 or 21-1023 ( 2-126 or 2-1022) (smallest exponent for normal numbers)

excess-127 representation The exponent can be computed from bits 24-31 by subtracting 127. If the exponent reaches -127 (binary 00000000), the leading 1 is no longer used to enable gradual underflow. excess-1023 representation The exponent can be computed from bits 53-63 by subtracting 1023. If the exponent reaches -1023 (binary 00000000000), the leading 1 is no longer used to enable gradual underflow.

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