Tiêu đề Lecture-2-Error Analysis and Computer Arithmetic.pdf ✅

Math 138 Numerical Analysis Example: Consider (111...1)2 with n consecutive 1’s to the left of the binary point. 111 ⋯ 1 # = 2&'( + 2&'# + ⋯ + 2( + 2* finite geometric series In a finite geometric series, 1 + + + +# + ⋯ + +, = 1 − +,.( 1 − + , + ≠ 1 ⇒ 2&'( + 2&'# + ⋯ + 2( + 2* = 1 − 2, 1 − 2 = 2, −1 ∴ 333 ⋯ 3 4= 45 − 3
Math 138 Numerical Analysis Hexadecimal Number System The hexadecimal number system represents all numbers as a sum of multiples of integer powers of 16. There are 16 digits, 0, 1, 2, ..., 9, A, B, C, D, E and F; and 16 is the base of the decimal system. Example: The number (AC.17)16 in the hexadecimal system represents the number IJ. 17 LM = 10 O 16L + 12 O 16Q + 1 O 16RL + 7 O 16RS LQ = 172.08984375 LQ IJ. 17 LM = 1010 1100. 0001 0111 S Example: Convert X = 110101.11001 S to hexadecimal. 110101.11001 S = 0011 0101.1100 1000 S = 35. J8 LM