(b) Convert (2AC),s to its decimal expansion Answer: (2AC)6 Show your work: (c)

Question

(b) Convert (2AC),s to its decimal expansion Answer: (2AC)6 Show your work: (c) Convert (100 1100 0011), to its hexadecimal expansion Answer. (100 1100 0011)2 Show your work (use the conversion table): (d) Convert (10 1011), to its octal expansion Answer: (10 1011)2 Show your work 4) Find the integer a such that (a) a - 89 (mod 19) and-9sas9. Answer: a- Show your work: (b) a -71 (mod 41) and 160 Sa 200. Answer: a- Show your work: (c) a 71 (mod 47) and -26 sas30. Answer: a- Show your work: 5) Give a recursive definition (with initial condition(s) of fan), n 1,2,3,... Answer: an Show your work: (b) an 4n -5, n 1,2, 3,... Answer: an Show your work: (c) an 5 Answer an Show your work:

Explanation / Answer

(2AC)16 are to be converted to decimal system;
= 2 * 162 + A * 161 + C * 160
= 2 * 256 + 10*16 + 12
= 512 + 160 + 12 = 684;
Thus, (2AC)16 is decimal system would be = 684;

4) a) 89 mod 19
= remainder when 89 is divded by 19
89 = 19*4 = + 13 or
89 = 19*5 -6
Since -9<=a<=9, we will take 89 = 19*5 - 6;
From this, we can see that 89 mod 19 = -6;

71 mod 41 for 160<=a<=200
71 = -123 + 194
71 = 41 (-3) + 194;
Thus, 71 mod 41 = 194;
Thus, a= 194

71 mod 47
71 = 47*1 + 24
Thus, 71 mod 47 = 24; a= 24

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