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Binary  Decimal

Binary  Decimal. Review. Each binary digit (bit) is a power of 2 Place the bits, multiply, and add Example: 11010110 2. Convert the following from binary to decimal. 1101 2 = ? 001101 2 = ? 10111010 2 = ?. Decimal  Binary. Decimal  Binary. Write out the powers of 2

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Binary  Decimal

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  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 = ?

  4. Decimal  Binary

  5. Decimal  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

  6. Examples 1510 = ? 4910 = ?

  7. Convert the following from decimal to binary 810 = ? 2510 = ? 8310 = ?

  8. Data Representation • Representing numbers is great, but what else is binary good for? • Umm…anything/everything • ASCII Example: • ASCII Table • ASCII  Binary Converter

  9. Data Representation • If we have 2 bits, how many different binary numbers can we make? • 00 • 01 • 10 • 11 • And if we had 3? • How about 4? • Umm...32?

  10. 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

  11. Pixel and Color Depth • Pixel ~ Picture element • What does an image look like when we zoom in? • An image is a matrix of numbers • Numbers ~ Colors • Number of bits restricts the number colors we can use (pixel/color depth) • Example: Lower your display setting’s color quality

  12. What is the maximum value? • If you had 2 bits? • 3 bits? • 4 bits? • What’s the pattern?

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