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Bits and Bytes

Bits and Bytes. Behind the scenes in your computer. All computer storage is organized into bytes. Think of each byte as a little storage bin Each byte is made up of 8 bits Each bit is an electronic circuit that is either on or off (off = 0, on = 1)

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Bits and Bytes

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  1. Bits and Bytes Behind the scenes in your computer

  2. All computer storage is organized into bytes • Think of each byte as a little storage bin • Each byte is made up of 8 bits • Each bit is an electronic circuit that is either on or off (off = 0, on = 1) • A specific sequence of 0’s and 1’s in a byte is called a bit pattern

  3. So, how many bytes are in your computer? Typical Capacities: RAM: 1, 2, 4, 6 or 8 GB Diskette: 1.44 MB Flash drive: 2, 4, 8, 16, 32, 64, 128 GB CD: 800 MB DVD: 4.7 GB Hard Drive: 500 GB – 2 TB

  4. Converting Between Units Example 2: 7.5 GB = ? KB 7.5 × 1,000,000,000 = 7,500,000,000 bytes 7,500,000,000 / 1000 = 7,500,000 KB Example 1: 5200 KB = ? MB 5200 × 1000 = 5,200,000 bytes 5,200,000 /1,000,000 = 5.2 MB

  5. You Try: 3.2 MB = ? Bytes 6.4 GB = ? MB 57,000 Bytes = ? KB 25,000 KB = ? MB

  6. What kinds of information do you store on your computer? • numerical values (binary number system) • text/character data (ASCII or Unicode) • program instructions (machine language) • images (jpg, gif, tiff, bmp, wmf, etc.) • video (mp4, mov, avi, wmv, etc.) • music (mp3, wav, wma, au, etc.)

  7. “Kathy Ames” is text It would be stored like this using ASCII codes

  8. Numerical values needed for arithmetic are stored using a different scheme The numerical value 40 would be stored like this using the binary number system. (note that “bit” stands for “binary digit”)

  9. How do binary numbers work? 8-bit binary number

  10. Converting from Binary to Decimal What is the decimal value of the bit pattern 01101010 ? Simple! Just add up the positional values where the 1’s appear: 64 + 32 + 8 + 2 = 106 So, we say that 011010102 = 106 decimal

  11. Converting from Decimal to Binary How can we represent the decimal value 151 in binary? Simple! Just think about money and consider positional values as bills and 151 “dollars” as the amount we must make. Then “count change” from largest “denomination” to smallest until total value of change is accumulated.

  12. Converting from Decimal to Binary How can we represent the decimal value 151 in binary? Running Total: 128

  13. Converting from Decimal to Binary How can we represent the decimal value 151 in binary? Running Total: 128

  14. Converting from Decimal to Binary How can we represent the decimal value 151 in binary? Running Total: 128

  15. Converting from Decimal to Binary How can we represent the decimal value 151 in binary? Running Total: 128 + 16 = 144

  16. Converting from Decimal to Binary How can we represent the decimal value 151 in binary? Running Total: 128 + 16 = 144

  17. Converting from Decimal to Binary How can we represent the decimal value 151 in binary? Running Total: 128 + 16 + 4 = 148

  18. Converting from Decimal to Binary How can we represent the decimal value 151 in binary? Running Total: 128 + 16 + 4 + 2 = 150

  19. Converting from Decimal to Binary How can we represent the decimal value 151 in binary? Running Total: 128 + 16 + 4 + 2 + 1 = 151 So, 151 decimal = 100101112

  20. So What is Hexadecimal?(often called “hex”) • A base 16 number system • 16 possible digits: 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F • Positional values are powers of 16 • Mainly used is as “short hand” for binary • 1 hex digit = 4 binary digits

  21. Hex Digits

  22. Converting from Hex to Decimal What is the decimal value of hex 3B? Simple! 3 × 16 + B × 1 = 3 × 16 + 11 × 1 = 48 + 11 = 59 So, we say that 3B hex = 59 decimal

  23. Converting from Hex to Decimal What is the decimal value of hex E4? Simple! E × 16 + 4 × 1 = 14 × 16 + 4 × 1 = 224 + 4 = 228 So, we say that E4 hex = 228 decimal

  24. Let’s take another look at Hex 3B So Hex 3B = 00111011 Binary (And note that 00111011 Binary = 32 + 16 + 8 + 2 + 1 = 59 Decimal)

  25. Let’s take another look at Hex E4 So Hex E4 = 11100100 Binary (And note that 11100100 Binary = 128 + 64 + 32 + 4 = 228 Decimal)

  26. What about converting Binary 10100010 to Hex?

  27. What about converting Binary 10100010 to Hex? So 10100010 Binary = A2 Hex

  28. Verify thatBinary 10100010 and Hex A2have the same Decimal values Binary 10100010 = 128 + 32 + 2 = 162 Hex A2 = A × 16 + 2 × 1 = 10 × 16 + 2 × 1 = 160 + 2 = 162

  29. You try: Convert 210 Decimal to: Binary: Hex: Convert 2D Hex to: Binary: Decimal: Convert 10001100 Binary to: Hex: Decimal:

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