Computer Science 1 Cheryl Dugas, PhD cadcs'rit'edu Bases

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Computer Science 1Cheryl Dugas, PhD
cad_at_cs.rit.eduBases
Haiku Cool to know although Not the same as
All your base are belong to us.
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Number Bases

• The most commonly used bases for numbers in
  computer science are
• Binary (base 2)
• Alphabet 0 1
• Example 10012, 01102, 02, 12
• Octal (base 8)
• Alphabet 0 1 2 4 5 6 7
• Example 78, 08, 4608
• Decimal (base 10)
• Alphabet 0 1 2 3 4 5 6 7 8 9
• Example 10010, 010, 200410
• Hexadecimal (base 16)
• Alphabet 0 1 2 3 4 5 6 7 8 9 A B C D E F
• Example 916, 016, ACDC16, DEADBEEF16

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Converting Number Bases to Decimal

• Consider the number 1810
• 1 101 8 100 1810
• Consider the number 100102
• 1 24 1 21 1810
• Consider the number 1216
• 1 161 2 160 1810

8
1
100
101
1
0
0
1
0
24
23
22
21
20
2
1
161
160
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Converting Decimal Numbers to Binary

• Consider the number 2710
• 201, 212, 224, 238, 2416, 2532
• Continually subtract the largest possible amount
  and place a 1 in the appropriate bit field
• 25 (0) too large
• 24 (1) ok, new value is 27-1611
• 23 (1) ok, new value is 11-83
• 22 (0) too large
• 21 (1) ok, new value is 3-21
• 20 (1) ok, new value is 1-10
• 2710 110112

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• Why do computer scientists get Halloween and
  Christmas mixed up?