Binary Decimal

1
Binary ? Decimal
2
Review

• Each binary digit (bit) is a power of 2
• Place the bits, multiply, and add
• Example 110101102

3
Convert the following from binary to decimal

• 11012 ?
• 0011012 ?
• 101110102 ?

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Decimal ? Binary
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Converting from Decimal to Binary

• Write out the powers of 2
• Subtract the largest power of 2 that is less than
  your number
• Make note of which power of 2 you subtracted with
  a 1 (unused powers of 2 will be 0)
• Subtract the next largest power of 2 from the
  result that you have
• Repeat until you reach 0
• Build your binary number from the 1s and 0s that
  you have placed

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Examples

• 1510 ?
• 4910 ?

7
Convert the following from decimal to binary

• 810 ?
• 2510 ?
• 8310 ?

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Data Representation

• If we have 2 bits, how many different binary
  numbers can we make?
• And if we had 3?
• How about 4?
• Umm...32?

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How many combinations?

• Each bit can only be a 0 or 1 (2 choices)
• The number of distinct combinations
• of n-bits is given by 2n

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Pixel Depth

• Pixel Picture element
• What does an image look like when we zoom in?
• An image is merely a matrix of numbers
• Numbers Colors
• Number of bits restricts the number colors we can
  use
• Example Lower your display settings color
  quality

11
What is the maximum value of a 16-bit integer?