Computer Number Representation The Challenge (12)10-1·23+1.22+0.2+0·20=(1100)2 (0.625)10=1.2-1+0.2-2+1.2-3=(0.101)2 (0.626)10=1.2-1+0.2-2+1.2-3+…=(0.101…)2 ≈(0.101)2 max range of number max significant digits ) finite number of bits of memory Weihua Gu (Shanghai Jiao Tong University) Computational Physics Chapter 1 14/09/20156/103Computer Number Representation The Challenge (12) 10 = 1 · 2 3 + 1 · 2 2 + 0 · 2 1 + 0 · 2 0 = (1100) 2 (0.625) 10 = 1 · 2 −1 + 0 · 2 −2 + 1 · 2 −3 = (0.101) 2 (0.626) 10 = 1 · 2 −1 + 0 · 2 −2 + 1 · 2 −3 + · · · = (0.101 · · ·) 2 ≈ (0.101) 2 max range of number max significant digits ↔ finite number of bits of memory Weihua Gu (Shanghai Jiao Tong University) Computational Physics Chapter 1 14/09/2015 6 / 103