Practice Solution 3 -- Storing Real Numbers

1. Convert the following numbers to standard scientific notation (place the decimal point just to the left of the most significant digit.)

   a.	3,405			_3.405 x 103______________
   
   b.	1,002,095		_1.002095 x 106___________
   
   c.	0.00357			_3.57 x 10-3______________
   
   d.	19.002			_1.9002 x 101_____________
   
   e.	6,902.005		_6.902005 x 103___________
   

2. Convert the following numbers which are stated in standard scientific notation to expanded form (our usual way of writing decimal numbers).

   a.	3.427001 x 103		__3427.001__________________
   
   b.	1.42 x 10-4		__.000142___________________
   
   c.	7.0001 x 106		__7,000,100_________________
   
   d.	6.5219 x 100		__6.5219____________________
   
   e.	1.139 x 10-5		__.00001139_________________
   

3. Assume that we are using the following system for storing real numbers. The system is defined as follows:
   

   bit 1:	sign, 0 for positive, 1 for negative
   bits 2-6:	exponent stored in excess-15 notation
   bits 7-16:	mantissa

   
   In order to determine what a real number would look like in memory (according to this system) you first convert the value to binary, then normalize it and use the number of positions you moved the radix point as the exponent. Be sure you represent the exponent in excess-15 notation.
   
   

   a.	What would 13.5 look like in memory?		____0100101011000000___
   
   b.	What would -88.3125 look like in memory?	____1101010110000101___
   
   c.	What value does 0100111100010000 represent?	____28 1/4______________
   

   
   
4. What is the ASCII representation, in decimal, hexadecimal, and binary of

   a.   The equal sign   __61____ (decimal)  ___3D____ (hex) __00111101___ (binary)
   
   b.   Lowercase z      _122____ (decimal)  ___7A_____ (hex) _01111010___ (binary)
   

   
   
5. Using the EBCDIC character set in Table 1.5 on page 62 of your text, and the memory dump of Figure 1.17b on page 60 of your text, what characters are at the following memory locations?

   a.      02A01B          _______-_____________________
   
   b.      02A024          _______._____________________
   
   c.      02A09F          _______"_____________________
   

6. Using the EBCDIC character set in Table 1.5 on page 62 of your text, and the memory dump of Figure 1.17b on page 60 of your text, specify the address of a memory location that contains the digit (as a character) that your social security number begins with.

                                  Address ___02A0A2____(my ssn starts with 2)___