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Chapter 2 Representing and Manipulating Information

Chapter 2 Representing and Manipulating Information. Bryant & O’Hallaron. 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 2 3 = 8. 2 2 = 4. 2 1 = 2. 2 0 = 1. [0001]. [0101]. [1011]. [1111]. – 2 3 = –8. 2 2 = 4. 2 1 = 2. 2 0 = 1. – 8. – 7. – 6.

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Chapter 2 Representing and Manipulating Information

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  1. Chapter 2Representing and Manipulating Information Bryant & O’Hallaron

  2. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 23 = 8 22 = 4 21 = 2 20 = 1 [0001] [0101] [1011] [1111]

  3. – 23 = –8 22 = 4 21 = 2 20 = 1 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 [0001] [0101] [1011] [1111]

  4. – 23 = –8 23 = 8 22 = 4 21 = 2 20 = 1 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 [1011] +16 [1111] +16

  5. 2w +2w–1 2w–1 0 0 –2w–1 Unsigned Two’s complement

  6. 2w +2w–1 2w–1 Unsigned Two’s complement 0 0 –2w–1

  7. – 23 = –8 – 22 = –4 22 = 4 21 = 2 20 = 1 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 7 8 [101] [1101] [111] [1111]

  8. x + y 2w+1 Overflow x +uy 2w Normal 0

  9. x + y +2w Positive overflow Case 4 x +ty +2w –1 +2w –1 Case 3 0 Normal 0 Case 2 –2w –1 –2w –1 Case 1 Negative overflow –2w

  10. 2m 2m–1 4 • • • 2 1 bm bm–1 • • • b2 b1 b0 . b–1 b–2 b–3 • • • b–n+1 b–n 1/2 • • • 1/4 1/8 1/2n–1 1/2n

  11. s exp frac s exp frac (51:32) Single precision 31 30 23 22 0 Double precision 63 62 52 51 32 0 31 0 frac (31:0)

  12. 1. Normalized s  0 &  255 f 2. Denormalized s 0 0 0 0 0 0 0 0 f 3a. Infinity s 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3b. NaN s 1 1 1 1 1 1 1 1  0

  13. – –10 –5 0 +5 +10 + Denormalized Normalized Infinity –0 +0 –1 –0.8 –0.6 –0.4 –0.2 0 +0.2 +0.4 +0.6 +0.8 +1 Denormalized Normalized Infinity

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