CPS120 Introduction to Computer Scence

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CPS120 Introduction to Computer Scence

• Computer Math Converting to Other Bases

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Converting Binary to Octal

• Groups of Three (from right)
• Convert each group
• 10101011 10 101 011
• 2 5 3
• 10101011 is 253 in base 8

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Binary to Hex

• Step 1 Form four-bit groups beginning from the
  rightmost bit of the binary number
• If the last group (at the leftmost position) has
  less than four bits, add extra zeros to the left
  of the group to make it a four-bit group
• 0110011110101010100111 becomes
• 0001 1001 1110 1010 1010 0111
• Step 2 Replace each four-bit group by its
  hexadecimal equivalent
• 19EAA7(16

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Converting Decimal to Other Bases

• Step 1 Divide the number by the base you are
  converting to (r)
• Step 2 Successively divide the quotients by (r)
  until a zero quotient is obtained
• Step 3 The decimal equivalent is obtained by
  writing the remainders of the successive division
  in the opposite order in which they were obtained
• Know as modulus arithmetic
• Step 4 Verify the result by multiplying it out

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Converting Decimal to Hexadecimal
222 13 0
16 3567 16 222 16 13 32
16 0
36 62 13 32 48
47 14 32
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D E F
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