The IEEE standard double-precision floating-point operand format consists of 64 bits. The sign occupies 1 bit, the exponent has 11 bits, and the fraction occupies 52 bits. The exponent bias is 1023 and the base is 2. There is an implied bit to the left of the binary point in the fraction. Infinity is represented with a biased exponent equal to 2047 and a fraction of 0.
(a) Give the formula for finding the decimal value of a normalized number.
(b) List a few biased exponents in binary, as is done in Table.
(c) Calculate the largest and smallest positive normalized numbers that can be accommodated.
Table Evaluating Biased Exponents
| Biased exponent e = E + 127 |
|
Exponent E in decimal | Decimal | Binary |
-126 | -126 + 127 =1 | 00000001 |
-001 | -001 + 127=126 | 01111110 |
000 | 000 + 127 = 127 | 01111111 |
+001 | 001 + 127 = 1258 | 10000000 |
+126 | 126 + 127 = 1253 | 11111101 |
+127 | 127 + 127 = 1254 | 11111110 |
We need at least 10 more requests to produce the solution.
0 / 10 have requested this problem solution
The more requests, the faster the answer.