=== MID TERM EXAM 2 ===
<code>
Screen 0 not modified     
 0 \                                              13:36JWB02/16/86 
 1 \ Last change:   Screen  011                   20:25JWB02/17/86 
 2                                                                 
 3                      MATHEMATICS  495                           
 4                                                                 
 5                                                                 
 6         INTRODUCTION TO THE FORTH PROGRAMMING LANGUAGE          
 7                                                                 
 8                                                                 
 9                       MID TERM EXAM                             
10                                                                 
11                     FEBRUARY 18, 1986                           
12                                                                 
13                     TOTAL  MARKS = 25                           
14                                                                 
15                                                                 


Screen 1 not modified     
 0 \ QUESTION 1 ( 5 MARKS )                       13:45JWB02/16/86 
 1 Show the resulting stack after return is pressed.               
 2                                                                 
 3 Example:   54  21  13   SWAP  DROP                              
 4  Answer:   54  13        <top of stack.                         
 5                                                                 
 6 a)  13  17  23  31   ROT    ROT                                 
 7                                                                 
 8 b)  13  31  17  23   OVER   OVER                                
 9                                                                 
10 c)  23  17  13   2   PICK   2  PICK  2  PICK                    
11                                                                 
12 d)  11  5  -14   5   /MOD                                       
13                                                                 
14 e)  25  50  10   */  5  +  10  /                                
15                                                                 


Screen 2 not modified     
 0 \ QUESTION 2 ( 5 MARKS )                       16:13JWB02/16/86 
 1 Design the FORTH word EIGHT that will draw  the outline of the  
 2 number eight on the display.  The outline must use the          
 3 word  WHITE  ( or WW )  from the CHECKER-BOARD  program.        
 4                                                                 
 5 : WHITE   177  EMIT  ;                        XXXXXX            
 6                                              X      X           
 7 The word EIGHT takes no stack parameters.    X      X           
 8 The output should look exactly like the      X      X           
 9 figure at right except that it will not       XXXXXX            
10 be made from X's.  To obtain full marks      X      X           
11 you should demonstrate your knowledge of     X      X           
12 factoring (ie  your definition of EIGHT      X      X           
13 should not be one great big word!).           XXXXXX            
14                                                                 
15                                                                 


Screen 3 not modified     
 0 \ QUESTION 3 ( 5 MARKS )                       16:15JWB02/16/86 
 1 A closed rectangular tank has a square base, b cm by b cm,      
 2 and is h cm high.                                               
 3 a) Write the word AREA that takes two stack inputs base, and    
 4    height and leaves the surface area, a= 2bb +4bh, on the stack
 5    AREA  ( b h   a )                                            
 6 b) Write the word VOLUME that takes two stack inputs base, and  
 7    height and leaves the volume, v=bbh, on the stack.           
 8    VOLUME ( b h  v )                                            
 9 c) Write the word TANK that takes two stack inputs base, and    
10    height and uses the words AREA and VOLUME above to produce   
11    the following report when executed as shown below:           
12    4 5 TANK                                                     
13    The surface area is  112  square centimeters.                
14    THe volume is   80  cubic centimeters.                       
15                                                                 


Screen 4 not modified     
 0 \ QUESTION 4 ( 5 MARKS )                       16:49JWB10/27/85 
 1 a) Show how you would create a FORTH variable called  VALVE  .  
 2    The variable VALVE will be used to contain the percentage    
 3    that a valve is open ( 0 is closed, 100 full open).          
 4                                                                 
 5 b) Design the word  STATUS?  to display the current valve state.
 6    ie  STATUS?    displays:   Valve is now  XX percent open.    
 7                                                                 
 8 c) Write  INITIAL-SETTING   that sets  variable   VALVE         
 9    to the top stack number.                                     
10                                                                 
11 d) Write the word OPEN which adds the top stack number to VALVE 
12    and word CLOSE which subtracts top stack number from VALVE . 
13 e) Can the value of VALVE ever become less than 0 using CLOSE ? 
14    Can the value of VALVE ever exceed 100 using OPEN ?          
15    Fix OPEN and CLOSE so that VALVE is always between 0 and 100.


Screen 5 not modified     
 0 \ QUESTION 5 ( 5 MARKS )                       16:19JWB02/16/86 
 1 a) Create an array called DATA that will hold 50 16bit numbers. 
 2                                                                 
 3 b) Write a word called CLEAR-DATA which initializes             
 4    each cell of the array DATA to zero.                         
 5                                                                 
 6 c) Write a word called COUNT-DATA that counts the number of     
 7    non zero entries in the array and saves it in the variable N.
 8                                                                 
 9 d) Write a word called SUM-DATA that leaves the sum of all non  
10    zero entries in the array DATA in the variable SSUM  .       
11                                                                 
12 e) Write a word called SUM-SQR that leaves the sum of squares   
13    of all non zero entries in the array DATA in the variable    
14     SSQR  .                                                     
15                                                                 


Screen 8 not modified     
 0 \  32 bit square root KS  4TH DIM V4N1P9                        
 1                                                                 
 2 : EASY-BITS ( drem1 partial.root1 count   drem2  partial.root2 )
 3     0  DO  >R  D2*  D2*                                         
 4            R@  -  DUP  0<                                       
 5            IF    R@ + R> 2*  1-                                 
 6            ELSE       R> 2*  3  +                               
 7            THEN  LOOP  ;                                        
 8                                                                 
 9 : 2'S-BIT ( drem2 proot2   drem3  proot3 ) \ get penultimate bit
10      >R  D2*  DUP  0<                                           
11      IF   D2*  R@  -  R>  1+                                    
12      ELSE D2*  R@  2DUP  U<                                     
13           IF   DROP  R> 1-                                      
14           ELSE  -    R> 1+                                      
15      THEN THEN ;                                                


Screen 9 not modified     
 0 \  32 bit square root KS  4TH DIM V4N1P9                        
 1 : 1'S-BIT   ( drem3 proot3   fullroot )  \ remainder lost       
 2      >R  DUP  0<                                                
 3      IF    2DROP  R>  1+                                        
 4      ELSE  D2*  32768 R@  DU<  0=  R>  THEN ;                   
 5 \ 32-bit unsigned radicand to 16-bit unsigned square root       
 6 : SQRT     ( ud     u  )                                        
 7         0  1 8 EASY-BITS  ROT  DROP  6 EASY-BITS                
 8         2'S-BIT  1'S-BIT  ;                                     
 9 \ Display square root of 16-bit number with 3 decimal places.   
10 : .SQRT  ( n   -- )  \ n  must be < 4096                        
11         16 *  62500  UM*                                        
12         SQRT  0 <#  # # #  ASCII . HOLD  #S #>                  
13         TYPE  SPACE ;                                           
14 : TEST  100 0 DO CR I 5 .R  SPACE I .SQRT  LOOP ;               
15                                                                 


Screen 11 not modified     
 0 \ ANSWER TO QUESTION 5  ( 5 MARKS )            20:25JWB02/17/86 
 1 Show the resulting stack after return is pressed.               
 2                                                                 
 3 Example:   54  21  13   SWAP  DROP                              
 4  Answer:   54  13        <top of stack.                         
 5                                                                 
 6 a)  13  17  23  31   ROT    ROT              13 31 17 23        
 7                                                                 
 8 b)  13  31  17  23   OVER   OVER             13 31 17 23 17 23  
 9                                                                 
10 c)  23  17  13   2   PICK 2 PICK 2 PICK      23 17 13 23 17 13  
11                                                                 
12 d)  11  5  -14   5   /MOD                    11  5  1 -3        
13                                                                 
14 e)  25  50  10   */  5  +  10  /             13                 
15                                                                 


Screen 12 not modified     
 0 \ ANSWER TO QUESTION NUMBER 2  ( 5 MARKS )     20:25JWB02/17/86 
 1                                                                 
 2 : WHITE   177  EMIT  ;                                          
 3 : .TOP  ( --  -- )                                              
 4         SPACE 6 0 ?DO WHITE LOOP ;                              
 5 : .ROW  ( --  -- )                                              
 6         WHITE 6 0 ?DO SPACE LOOP WHITE ;                        
 7                                                                 
 8 : EIGHT ( --  -- )                                              
 9         CR .TOP                                                 
10         3 0 DO CR .ROW LOOP                                     
11         CR .TOP                                                 
12         3 0 DO CR .ROW LOOP                                     
13         CR .TOP                                                 
14         CR  ;                                                   
15                                                                 


Screen 13 not modified     
 0 \ ANSWER TO QUESTION 3  ( 5 MARKS )            18:04JWB02/16/86 
 1  : AREA ( b h   a )                                             
 2      OVER DUP *  2 * ROT ROT  * 4 * +  ;                        
 3                                                                 
 4  : VOLUME ( b h   v )                                           
 5      OVER * *  ;                                                
 6                                                                 
 7  :  TANK ( b h  --  )                                           
 8    CR OVER OVER                                                 
 9    CR ." The surface area is " AREA .                           
10       ." square centimeters."                                   
11    CR ." The volume is " VOLUME .                               
12       ." cubic centimeters."                                    
13    CR  ;                                                        
14     4   5    TANK                                               
15                                                                 


Screen 14 not modified     
 0 \ ANSWER TO QUESTION 4 ( 5 MARKS)              20:22JWB02/17/86 
 1 ( a) VARIABALE  VALVE                                           
 2                                                                 
 3 ( b) : STATUS? ( --  -- )                                       
 4          CR ." Valve is now  " VALVE @ . ." percent open." ;    
 5                                                                 
 6 ( c) : INITIAL-SETTING  ( n  -- )                               
 7          0 MAX 100 MIN  VALVE ! ;                               
 8                                                                 
 9 ( d) : OPEN  ( n  -- )          VALVE +! ;                      
10      : CLOSE ( n  -- )  NEGATE  VALVE +! ;                      
11                                                                 
12 ( e) : OPEN  ( n  -- )  VALVE @    + 100 MIN VALVE ! ;          
13      : CLOSE ( n  -- )  VALVE @ SWAP - 0 MAX VAVLE ! ;          
14                                                                 
15                                                                 


Screen 15 not modified     
 0 \ ANSWER TO QUESTION 5:  ( 5 MARKS )           18:36JWB02/16/86 
 1 ( a) CREATE  DATA  100 ALLOT                                    
 2 ( b)  : CLEAR-DATA ( --  -- )                                   
 3           DATA  100 0  FILL ;                                   
 4 ( a)  VARIABLE N   VARIABLE SSUM     VARIABLE SSQR              
 5  : DATA@ ( i  -- )                                              
 6      DATA SWAP 2* + @ ;                                         
 7 ( c)                                                            
 8  : COUNT-DATA ( --   -- ) 0 N !                                 
 9    50 0 DO I DATA@ IF 1 N +! THEN LOOP  ;                       
10 ( d)                                                            
11  : SUM-DATA  ( --   -- ) 0 SSUM !                               
12    50 0 DO I DATA@ ?DUP IF SSUM +!  THEN  LOOP ;                
13 ( e)                                                            
14  : SUM-SQR  ( --  -- ) 0 SSQR !                                 
15    50 0 DO I DATA@ ?DUP IF DUP * SSQR +!  THEN  LOOP ;  -->     


Screen 16 not modified     
 0 \  Used for testing solution.                  18:34JWB02/16/86 
 1                                                                 
 2      : #IN  QUERY  INTERPRET ;                                  
 3      : ENTER-DATA ( --  -- )                                    
 4        CLEAR-DATA  0  BEGIN                                     
 5        CR DUP . ASCII > EMIT  #IN DUP 0<>                       
 6        WHILE  OVER 2* DATA + ! 1+ REPEAT  2DROP ;               
 7                                                                 
 8                                                                 
 9                                                                 
10                                                                 
11                                                                 
12                                                                 
13                                                                 
14                                                                 
15                                                                 

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