CS 301 Fall 2002 Number Systems

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CS 301 Fall 2002Number Systems

• Slide Set 1

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Bits, Bytes, and Words

• A bit (binary digit) is 0 or 1
• byte 8 bits
• word 2 bytes (16-bit)
• doubleword 2 words (32-bit)
• quadword 4 words (64-bit)
• kilobyte (K) 210 (1024) bytes
• megabyte (M) 220 (1048576) bytes

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Binary numbers

• Bit 7 6 5 4 3 2 1 0
• Value 128 64 32 16 8 4 2 1
• Example 01000101 69

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Negative Binary Numbers

• Ones complement flip the bits 1 becomes 0, 0
  becomes 1.
• Twos complement take ones complement, then add
  one. This is how the computer represents the
  negative.
• Why? Because it works.Try -0, -1, and -13. (Check
  that adding -13 to 13 gives you 0)
• Actually, it works because when you add anything
  to its ones complement, you get all ones. Adding
  one to that gives you 0 (with a carry out).

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Hexadecimal representation

• Base 16 Digits are 0123456789ABCDEF
• Write with a trailing h 4A1Fh

Decimal Binary Hex Decimal Binary Hex
0 0000 0 8 1000 8
1 0001 1 9 1001 9
2 0010 2 10 1010 A
3 0011 3 11 1011 B
4 0100 4 12 1100 C
5 0101 5 13 1101 D
6 0110 6 14 1110 E
7 0111 7 15 1111 F
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Hex and Binary Arithmetic

• Just as decimal. Add corresponding columns, if
  the result is higher than the base, then carry.
• To subtract, either use twos complement to find
  the negative and then add, or do as in base 10
  (borrow instead of carry)

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Memory

• 01000001 Is it 65 or A (ASCII) or floating
  point or something else?
• However you look at it.