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CSE111: Great Ideas in Computer Science

CSE111: Great Ideas in Computer Science. Dr. Carl Alphonce 219 Bell Hall Office hours: M-F 11:00-11:50 645-4739 alphonce@buffalo.edu. Announcements. No recitations this week. First meeting of recitations in week of 1/25-1/29.

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CSE111: Great Ideas in Computer Science

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  1. CSE111: Great Ideas in Computer Science Dr. Carl Alphonce 219 Bell Hall Office hours: M-F 11:00-11:50 645-4739 alphonce@buffalo.edu

  2. Announcements • No recitations this week. First meeting of recitations in week of 1/25-1/29. • Extra copies of syllabus available at course web-site (address is on UB Learns).

  3. cell phones off (please)

  4. Agenda • Review from last class • same data, different encodings • Today’s topics • binary numbers

  5. Review • Color encoding • RBG vs. CMYK encodings • Number encoding • base 10 vs. base 2 • Same information can be encoded in many different ways.

  6. Counting Decimal (base 10) Binary (base 2) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 etc. 0 1 10 11 100 101 110 111 1000 1001 1010 1011 1100 1101 etc.

  7. Number systems Decimal (base 10) Binary (base 2) Each position is weighted by a power of 2. E.g. 111 = 1*4 + 1*2 + 1*1 = “seven” 1*22 + 1*21 + 1*20 E.g. 1101 = 1*8 + 1*4 + 0*2 + 1*1 = “thirteen” 1*23 + 1*22 + 0*21 + 1*20 • Each position is weighted by a power of 10. • E.g. 734 = • 7*100 + 3*10 + 4*1 • 7*102 + 3*101 + 4*100 • E.g. 1101 = • 1*1000 + 1*100 + 0*10 + 1*1 • 1*103 + 1*102 + 0*101 + 1*100

  8. Bit string • A ‘0’ or ‘1’ is a binary digit, or a bit. • A sequence of bits is called a bit string. • For example: • 00001101 is a bit string • As numbers: ‘0’ is zero, ‘1’ is one • Reality • just two symbols • In hardware: two different voltage levels

  9. Binary Arithmetic • Operations in base 2 work the same as in base 10. • Addition: 2 + 3 = 5 10 +11 101

  10. Exercises • Compute the following sums, in base 2 5 + 1 = 6 8 + 8 = 16 10 + 12 = 22

  11. Setting up the exercises • Compute the following sums, in base 2 5 + 1 = 6 8 + 8 = 16 10 + 12 = 22 101 1000 1010 + 001+ 1000+ 1100

  12. Solving up the exercises • Compute the following sums, in base 2 5 + 1 = 6 8 + 8 = 16 10 + 12 = 22 101 1000 1010 + 001+ 1000+ 1100 110 10000 10110

  13. Interpretation • QUESTION: • What does 1101 represent?

  14. Interpretation • QUESTION: • What does 1101 represent? • ANSWER: • Whatever we want it to represent!

  15. Encoding Schemes • RGB / CMYK (colors) • Binary (non-negative numbers) • Two’s complement (integers) • IEEE 754 (approx. floating point numbers) • ASCII / EBCDIC / Unicode (characters) • GIF / BMP / JPG (images) • MP3 / CD (audio) • MPEG-2 / MPEG-4 (video – e.g. BluRay and HDTV)

  16. Fixed-width encodings • Suppose we have a four-bit wide representation. • We then have 24 = 2*2*2*2 = 16 distinct bit patterns:

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