Real Numbers

The 8087 stores real numbers in a three-field binary format that resembles scientific, or exponential, notation. The number's significant digits are held in the significand field, the exponent field locates the binary point within the significant digits (and therefore determines the number's magnitude), and the sign field shows whether the number is positive or negative. (The exponent and significand are analogous to the terms "characteristic" and "mantissa" sometimes used to describe floating-point numbers). Negative numbers differ from positive numbers only in their sign bits.

The 8087 carries the digits of the significand in normalized form. This means that except for the value zero, the significand is an integer and a fraction as follows:

1  FFF...FF

where  shows an assumed binary point. The number of fraction bits varies according to the real format: 23 for short, 52 for long and 63 for temporary real. By normalizing real numbers so that their integer bit is always a 1, the 8087 eliminates leading zeros in small values. This technique maximizes the number of significant digits that can be accommodated in a significand of a given width.

Note: In the short and long real formats the integer bit is implicit and is not really stored; the integer bit is physically present in the temporary real format only.

If one were to examine only the significand with its assumed binary point, all normalized real numbers would have values between 1 and 2. The exponent field locates the actual binary point in the significant digits. Just as in decimal scientific notation, a positive exponent has the effect of moving the binary point to the right and a negative exponent moves the binary point to the left, inserting leading zeros as necessary. An unbiased exponent of zero shows that the position of the assumed binary point is also the position of the actual binary point. The exponent field, then, determines a real number's magnitude.

To simplify comparing real numbers, the 8087 stores exponents in a biased form. This means a constants is added to the true exponent. The value of this bias is different for each real formal. It has been chosen to force the biased exponent to be a positive value. This allows the real numbers, of the same format and sign, to be compared as if they are unsigned binary integers. That is, when comparing them bit-wise from left to right beginning with the leftmost exponent bit, the first bit position that differs orders the numbers. No further comparison is needed. A number's true exponent can be determined simply by subtracting the bias value of its format.

The short and long real formats exist only in memory. If a number in one of these formats is loaded into a 8087 register, it is converted to temporary real, the format used for the 8087 internal operations.

Likewise, data in 8087 registers can be converted to short or long real for storage in memory. The temporary real format can be used in memory also, typically to store intermediate results that cannot be held in 8087 registers.

Notes:

notation запись; представление

significand field поле мантиссы

integer целое число

fraction дробь; дробная часть

leading zeros нулевые старшие разряды

bias смещение; сдвиг

IX. Переведите предложения, обращая внимание на ing-forms.

1. The system performs diagnostics of the system and displays the size of the memory being tested.

2. Entering the wrong disk drive TYPE causes improper operation of the disk.

3. The 286 LX baby board contains an 80286 processor running at 12MHz with a processor clock cycle time of 83.3ns, and an average memory cycle time of 175ns.

4. A machine time being a costly proposition, an operator must be able to make a quick distinction between machine malfunction and errors occurring in the program.

5. The software installation procedure is completely dependent on the program being used.

6. Editing consists of painting pixels with selected colors.

7. When editing is complete, move the cursor to the small view box.

8. An alternative to typing filenames when storing or retrieving file is to use the question mark.

9. Multiplexing of the 14 address lines onto the seven address pins is done with an 13242 multiplexer.

10. Ну monitoring address lines during the first quarter cycle the generator knows when the processor does not require access to memory.

11. The program works by adding together the least-significant digits in locations 51 and 53 first and storing the result in 55.

12. These processors have 16 bit addition and subtraction facilities which make multiple-precision arithmetic much faster using shorter programs.

X. Переведите предложения, обращая внимание на выделенные слова.

a result результат; следствие

as a result в результате

to result in приводить к; давать в результате

to result from вытекать из; являться результатом

1. After performing computations a computer displays the result.

2. The detection of errors in a program results in a program interruption.

3. These data result from the comparison operation.

4. The importance of microprocessors results from their ability to process information with high speeds.

5. The change in velocity resulted from the force acting from outside.

6. Their experiments resulted in the discovery of argon.

7. If we plot these parameters a straight line results.

8. The application of the method results in the following formula.

rather + прилагательное довольно

rather than а не

1. This rather simplified model will account for our observation.

2. These values show some rather interesting features.

3. These uniform fields are the exception rather than the rule.

4. The explanation offered was rather uncertain.

5. In this case the energy appears as electrical energy rather than as heat, energy.

6. As these data was rather unreliable, we tried to verify them in our laboratory.

7. In this case mathematical methods would have to be employed rather than graphical ones.

XI. Обратите внимание на значение следующих слов.

a number число; количество; номер

to number насчитывать

a number of ряд; несколько; множество

1. The students' body of our university numbers more than seven thousand students.

2. The first automatic digital computer could add numbers at the speed of 5000 additions per second.

3. There are in existence a number of general simulation programs which deal with certain problems.

4. The binary point separates a number into a whole part and a fraction.

5. Production of the computer itself involved the efforts of a number of electronic engineers, mathematicians, and other specialists.

6. The position to the left of the binary point is used to indicate the sign of the number. A 0 indicates a positive number and a 1 a negative number.