Single-precision floating-point format (sometimes called FP32 or float32) is a computer number format, usually occupying 32 bits in computer memory; it represents a wide dynamic range of numeric values by using a floating radix point.

A floating-point variable can represent a wider range of numbers than a fixed-point variable of the same bit width at the cost of precision. A signed 32-bit integer variable has a maximum value of 231 1 = 2,147,483,647, whereas an IEEE 754 32-bit base-2 floating-point variable has a maximum value of (2 223) 2127 3.4028235 1038. All integers with 7 or fewer decimal digits, and any 2n for a whole number 149 n 127, can be converted exactly into an IEEE 754 single-precision floating-point value.

The representation of a signed real number includes an integer portion, a fractional portion, and an exponent. Use floating-point constants to represent floating-point values that can't be changed. You can omit either the digits before the decimal point (the integer portion of the value) or the digits after the decimal point (the fractional portion), but not both. You may leave out the decimal point only if you include an exponent (e|E). No white-space characters can separate the digits or characters of the constant. A floating-point constant without an f, F, l, or L suffix has type double. If the letter f or F is the suffix, the constant has type float. If suffixed by the letter l or L, it has type long double.

The following examples illustrate some forms of floating-point constants and expressions:

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15.75L

1.575E1 /* = 15.75 */

1575e-2 /* = 15.75 */

-2.5e-3F /* = -0.0025 */

25E-4 /* = 0.0025 */

4. (15 points) Create a regular expression, DFA, and Regular Grammar for the floating point constant.

5. (5 points) Analyze the above problem for the 4 language criteria.