CST-111 Exam #1 k1-tb+
"Introduction to Information Technology" 		YOUR_NAME:____K_E_Y_____
Section 1X1 CRN=XXXXX
    1. List all possible combinations of three bits. . . . . 000 001 010 011 100 101 110 111

    2. How much is 47 plus 35 Assuming both numbers are octal? . . . . 478 + 358 = 1048
    3. How much is 47 plus 35 . . . Assuming both numbers are hexadecimal? . . . . 47G + 35G = 7CG

    4. How much is 1011 plus 110 . . . Assuming both numbers are binary? . . . . 10112 + 1102 = 100012
    5. Now, convert the answer to hexadecimal. . . . . 11G
    6. And, convert the answer to octal. . . . . 218

    7. What is this value in base nine? . . . . 189

    8. What is this value in base three? . . . . 1223
  2. Write your first, middle, and last initials in the 3 boxes below. (If you don't have a middle initial, make one up.) For each (UPPER CASE) letter, write the ASCII code value,

    in decimal, hexadecimal, octal, and binary.
    Initial Decimal Hex Octal Binary
    First
      K  
    		75 4BG 1238 0100 10112
    Middle
      E  
    		69 45G 1058 0100 01012
    Last
      Y  
    		89 59G 1318 0101 10012
  3. Copy the decimal values, for each of the above initials. (We'll refer to these as A, B, and C.) Then, create three new values (X, Y, Z) by adding ten to the first number, subtracting five from the second number, and adding 33 to the third number.

    In the table below, show the ASCII character represented by each new number (X,Y,Z), as well as the value in hex and binary. In the last column, COMPLEMENT the 8-bit binary value (i.e. change every one to a zero, and every zero to a one).

    Old Decimal New Decimal ASCII Hex Binary Complement
    X=A+10  _75_+10
      85  
    		U 55G 0101 01012 1010 10102
    Y=B-5  _69_-5
      65  
    		A 41G 0100 00012 1011 11102
    Z=C+33  _89_+33
      122  
    		z(lower-case) 7AG 0111 10102 1000 01012
  4. In the table below, copy the binary COMPLEMENTs for X, Y, and Z, from the above table,
    What negative values (decimal) would these bits represent, for each representation scheme?
    Complement (Copy_from_above) Ones- complement Twos- complement Sign- Magnitude Offset- 128
    X'
    1010 10102
    		-85 -86 -42 -86
    Y'
    1011 11102
    		-65 -66 -62 -66
    Z'
    1000 01012
    		-122 -123 -5 -123
  5. This question asks you to consider a few colors created by using the above binary values (X, Y, Z, and X', Y', Z') for the three bytes used by the "TrueColor" representation scheme, with one byte for each RGB value.


    1. How many bits are needed to have a different code for each student at SCCC,
      assuming that there are approximately 20,000 students. . . . 15 bits = log2 20,000

    2. What number of students would require more bits? . . . 32,760 . . . NOTE:   214=16,384 < 20,000 < 215=32,768

    3. How many bits are needed to give each citizen of the U.S.A. a different code, . . . 29 bits ( log2 300M )
      assuming the population is just over 300 million.

    4. What size population would require more bits? . . . over 512 million . . . NOTE:   228~=256M, 229~=512M,

    5. How many (different) memory addresses can be addressed with a 20-bit address? . . . 1 million (approx.)

    6. How many (different) memory addresses can be addressed with a 21-bit address? . . . 2 million (approx.)

    7. How many bits are needed to address a 5 Gigabyte memory? . . . 33 bits ( log2 5G ) . . . NOTE:   232=4G, 233=8G
    1. How many picoseconds are there in five minutes? . . . 300,000,000,000,000 ( 1 trillion picoseconds per second; 300 sec. / 5 min.)

    2. How many cycles are executed per second by a 5 ns CPU
      (i.e. a processor that has a cycle-time of five nanoseconds)? . . . 200,000,000 ( 1 billion nanoseconds per second; divided by 5)

    3. If another processor is ten times a fast, then how long does it take to perform one cycle. . . . 500 pico-seconds ( i.e., one-tenth of 5 ns = 0.5 ns = 500 ps )
      NOTE: Do not use any fractions, decimal points, or powers of ten, in your answer.

    4. How would you describe the speed of the faster processor, specified in Hertz units? . . . 2 GigaHertz ( two-billion cycles per second )

    5. How would you describe the speed of the slower processor, specified in Hertz units? . . . 200 MegaHertz ( two-hundred-million per second )
  8. A B output
    0 0   0
    0 1   1
    1 0   1
    1 1   0
    For the expression given below, draw a circuit that performs this operation and create a truth-table for the output.   (Prime ' indicates negation). 
         A B'    +    A' B  
 
 
 
 
 
 
 
 
  9. A B output
    0 0   0
    0 1   1
    1 0   1
    1 1   0
    For the expression given below, draw a circuit that performs this operation and create a truth-table for the output.   (Prime ' indicates negation). 
        [ (A' + B)    &    (A + B') ] '
 
 
 
 
 
 
 
 
  10. Compare the above two truth tables. What principle(s) are illustrated?
       Equivalence.   (Same truth-table.)
       DeMorgan's Law.   (Apply to one Boolean expression to yield the other, and vise-versa.)
  11. [Extra credit]  Examine the following logical expressions.   Can you explain WHY a computer would contain many circuits that perform either of these operations ? 
    	 
	 ABC  +  AB'C'  +  A'BC'  +  A'B'C 
	 111     1           1           1		(odd)

	 ABC  +  ABC'   +  AB'C   +  A'BC 
	 111     11        1  1        11 		( >= 2 )
        Both could be used in adder circuits.
        One computes the result (1 iff odd), the other computes the carry-out (1 iff 2 or greater).