Exercises I / 5.1
  1. Write a number expressed in Hindu-Arabic numerals which corresponds to each of the following numbers written with Roman numerals:
    1. DC
    2. XXXIX
    3. XLVIII
    4. DCCLXXV
    5. CMII
    1. M
    2. VDLV
    3. MMCXCIV
    4. LVMMDLI
    5. XCXI

     
  2. Write a number expressed in Roman numerals which corresponds to each of the following numbers written with Hindu-Arabic numerals:
    1. 101
    2. 1492
    3. 2000
    4. 2006
    5. 44
    1. 333
    2. 5000
    3. 100,000
    4. 105,000
    5. 9999

     
  3. Performing arithmetic operations with Roman numbers is not a simple task.  Write the result of each of the following operations as a number expressed in Roman numerals:
    1. XLIX + LXVI
    2. X - MMMDCCXC
    3. XXXIII × IV
    4. CXLIV ÷ XII

     
  4. Convert each of the following numbers from binary (base 2) notation to decimal (base 10) notation:
    1. 10
    2. 11
    3. 101
    4. 111
    5. 1011
    1. 1111
    2. 10111
    3. 11111
    4. 101111
    5. 111111

     
  5. Convert each of the following numbers from decimal (base 10) notation to binary (base 2) notation:
    1. 5
    2. 10
    3. 25
    4. 64
    5. 100
    1. 128
    2. 200
    3. 255
    4. 1024
    5. 2000

     
  6. Convert each of the following numbers from hexadecimal (base 16) notation to decimal (base 10) notation:
    1. 10
    2. 11
    3. 1F
    4. AB
    5. FF
    1. F00
    2. 100
    3. 1F1
    4. FFF
    5. ABC

     
  7. Convert each of the following numbers from decimal (base 10) notation to hexadecimal (base 16) notation:
    1. 10
    2. 100
    3. 255
    4. 224
    5. 127
    1. 200
    2. 1024
    3. 1000
    4. 2006
    5. 10,000

     
  8. Convert each of the following numbers from binary (base 2) notation to hexadecimal (base 16) notation:
    1. 1
    2. 10
    3. 101
    1. 10000
    2. 1000 0000
    3. 1111 1111

     
  9. Convert each of the following numbers from hexadecimal (base 16) notation to binary (base 2) notation:
    1. 10
    2. A
    3. F
    1. 99
    2. AB
    3. FF

     
  10. Convert each of the following numbers (from the given base to the indicated base):
    1. 10.1(base 2)   =   _______ (base 10)
    2. 11.11(base 2)   =   _______ (base 10) 
    3. A.1(base 16)   =   _______ (base 10) 
    4. B2.F(base 16)   =   _______ (base 10) 
    5. 16.5(base 10)   =   _______ (base 2) 
    6. 16.75(base 10)   =   _______ (base 2) 
    7. 16.0625(base 10)   =   _______ (base 16) 
    8. 16.5(base 10)   =   _______ (base 16) 
    9. D.8(base 16)   =   _______ (base 2) 
    10. 101.01(base 2)   =   _______ (base 16) 
Solutions — Exercises I / 5.1

  1.  
    1. 600
    2. 39
    3. 48
    4. 775
    5. 902
    1. 1,000,000
    2. 5555
    3. 2194
    4. 57,551
    5. 10,111

  2.  
    1. CI
    2. MCDXCII
    3. MM
    4. MMVI
    5. XLIV
    1. CCCXXXIII
    2. V
    3. C
    4. CV
    5. MXCMXCIX

  3.  
      CXV
    1. VMCCX
    2. CXXXII
    3. XII

  4.  
    1. 2
    2. 3
    3. 5
    4. 7
    5. 11
    1. 15
    2. 23
    3. 31
    4. 47
    5. 63

  5.  
    1. 101
    2. 1010
    3. 11001
    4. 1000000
    5. 1100100
    1. 1000 0000
    2. 1100 1000
    3. 1111 1111
    4. 100 0000 0000
    5. 111 1101 0000

  6.  
    1. 16
    2. 17
    3. 31
    4. 171
    5. 255
    1. 3840
    2. 256
    3. 497
    4. 4095
    5. 2748

  7.  
    1. A
    2. 64
    3. FF
    4. E0
    5. 7F
    1. C8
    2. 400
    3. 3E8
    4. 7D6
    5. 2710

  8.  
    1. 1
    2. 2
    3. 5
    1. 10
    2. 80
    3. FF

  9.  
    1. 10000
    2. 1010
    3. 1111
    1. 1001 1001
    2. 1010 1011
    3. 1111 1111

  10.  
    1. 2.5
    2. 3.75
    3. 10.0625
    4. 178.9375
    5. 10000.1
    6. 10000.11
    7. 10.1
    8. 10.8
    9. 1101.1
    10. 5.4