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UIT2201: Tutorial Set 7 (Spring 2013)
(Solution Sketch to Selected Problems)
** NOT TO BE GIVEN TO FUTURE UIT2201 STUDENTS **

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T7-D1: (Binary Representations)
DIY (See solution sketch for T7-Q1.)

T7-D2: (ASCII and UNICODE encoding) -- SOLUTION SKETCH

      Message: "My secret spot in U-Town" (Do not include the surrounding "" marks.)

(a) in ASCII code --- 24 bytes = 24x8 bits = 192 bits
(b) in UNICODE --- 48 bytes = 48x8 bits = 384 bits
(Note: Count everything between ""; spaces, punctuations, etc.)

• Problem 1(b): (367)₄ = 3x8² + 6x8¹ + 7x8⁰ = 192 + 48 + 7 = 247
• Problem 1(c): (1BA)₁₆ = 1x16² + 11x16¹ + 10x16⁰ = 256 + 176 + 10 = 442

• Problem 3(b): (110001)_2,unsigned = 1x2⁵ + 1x2⁴ + 1x2⁰ = 32 + 16 + 1 = 49

• Problem 3(c): (1111111)_2,bunsigned = 1x2⁶ + 1x2⁵ + 1x2⁴ + 1x2³ + 1x2² + 1x2¹ + 1x2⁰ = 127

• Problem 4(c): (275)₁₀ = (100010011)_2,signed; But this needs 9 bits (> 8); Overflow

• Problem 5(a): (10 0011 0001)_2,signed = – (2⁵ + 2⁴ + 2⁰) = – (32+16+1) = – 49

• Problem 5(d): (10 0000 0000)_2,signed = – 0 (also equal to 0)

• Problem 8(b): – (20.25)₁₀ = – (10100.01)₂ = – (0.1010001) x 2⁵ = – (0.1010001) x 2^+(101)₂
      [Note: (0.25)₁₀ = (0.01)₂]

  Internal Representation:

  1 1 0100 0100 0 0 0101

• Problem 9:

  9(b):  Mike  = 01001101  01101001  01101011  01100101
                    M         i         k         e 
  
  9(d): (a+b)  = 00101000  01100001  00101011  01100010  00101001
                     (         a         +         b        ) 
  

(Colour digital picture: true colour with 24 bits per pixel)
(a) Uncompressed:  (16 x 106) x 24 bits = 384 x 106 bits = 48 x 106 bytes 
     A 8-GBytes memory stick can store 8*230 / 48 x 106 = 178.957 images
        namely  178 images

(b) Compressed 20:1 ratio: 178.957 x 20 = 3579 songs

(MP3 format sound) 3 minute song
     [From textbook, MP3 format: sample rate 44,100 and bit depth 16 bits]
(a) Uncompressed:   44100 samples/sec x 16 bits/sample x (60 x 3) sec = 127,008,000 bits
                       = 127,008,000/(220) M-bits = 15.14 MBytes
     A 8-GB memory stick can store about 541 songs (3mins per song)
                8GB/15.14 MBytes = 8*1024MBytes / 15.14MBytes = 541.1
 
(b) With compression ratio 11:1 ratio: 127,008,000/11 = 11,546,181.8 bits = 1.37641 MBytes
     A 1-GB memory stick can store 8*1024MBytes / 1.376MBytes = 5951 songs