Digital aritmetik: Multiplikation och division. Talrepresentation

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Heltals-representation kan orsaka overflow • Addition: • Multiplication: (011) 2 + (010) 2 = (101) 2 (011) 2 * (010) 2 = (110) 2 (3) 10 + (2) 10 = (-3) 10 (3) 10 * (2) 10 = (-2) 10 (011) • Subtraction: 2 * (011) 2 = (001) 2 (3) (110) 2 - (011) 2 = (011) 10 * (3) 10 = (1) 10 2 (-2) 10 - (3) 10 = (3) 10 p. 27 - IE1204 Digital Design - F6 - Johnny Öberg, ICT/ES Fixed-Point Numbers Två-komplementsrepresentation B=b N-1 . b N-2 ...b 1 b 0 where b i ∈{0,1} b N-1 b N-2 ... b 1 b 0 Sign Bit Fixed-Point Value FiP(B)=-b N-1 2 0 +b N-2 2 -1 +...+b 1 2 -(N-2) +b 0 2 -(N-1) Detta format kallas också för Q N-1 -format eller fractional representation p. 28 - IE1204 Digital Design - F6 - Johnny Öberg, ICT/ES
Fixed-Point Q2-Representation 000 111 0 001 -0.25 0.25 110 -0.5 0.5 010 -0.75 0.75 101 -1 011 100 p. 29 - IE1204 Digital Design - F6 - Johnny Öberg, ICT/ES Multiplikation i Q-formatet • Multiplikation orsakar inte overflow i Q-formatet, men kan resultera i förlust av precision (1.10) 2 * (0.11) 2 = (1.1010) 2 (Q4-format) = (1.10) 2 (Q2-format) Generellt: b 2 b 1 b 0 Q2 * b 2 b 1 b 0 Q2 Utökade teckenbitar b 5 b 4 b 3 b 2 b 1 b 0 Q4 p. 30 - IE1204 Digital Design - F6 - Johnny Öberg, ICT/ES
Page 1 and 2: F6 : Digital Aritmetik II Talrepres
Page 3 and 4: Multiplikation med en teckenbit Tec
Page 5 and 6: Eller så gör vi det enkelt för o
Page 7 and 8: Multiplikation med 2 0101*2=1010 (5
Page 9 and 10: Division mellan två (positiva) hel
Page 11 and 12: Using a multiplier and a ROM for di
Page 13: Division med 2 n 1010/2=101 (10/2=5
Page 17 and 18: IEEE-754 • Flyttals-standarden IE
Page 19 and 20: Multiplikation med flyttal • Give
Page 21 and 22: Fixed-Point vs. Floating-Point •
Page 23: Flyt-tal (eng. Floating Point) •

Digital aritmetik: Multiplikation och division. Talrepresentation

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