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Understanding Data Encodings in Computer Science: A Review of Binary and Color Systems

In this lecture, Dr. Carl Alphonce explores the diverse ways information can be encoded in computer systems. He reviews binary numbers and introduces concepts like RGB and CMYK color encodings, as well as the differences between base 10 and base 2 number systems. Through arithmetic exercises and discussions, students will gain a stronger grasp of how data is represented using binary, as well as understand encoding schemes used in various media formats. This session provides a foundational understanding crucial for further studies in computer science.

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Understanding Data Encodings in Computer Science: A Review of Binary and Color Systems

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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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