Recall that the greatest common divisor of two integers a and b, GCD(a, b), not both of which are zero, is the largest positive integer that divides both a and b. The Euclidean algorithm for finding this greatest common divisor of a and b is as follows:
- Divide a by b to obtain the integer quotient q and remainder r so that a = bq + r. Note: if b = 0, then GCD(a, b) = a.
- Now, GCD(a, b) = GCD(b, r) so replace a with b and b with r, and repeat this procedure
Since the remainders are decreasing, eventually a remainder of 0 will result. The last nonzero remainder is GCD(a, b). For example,
1260 = 198 x 6 + 72 GCD(1260,198) = GCD(198,72)
199 = 72 x 2 + 54 GCD(1260,198) = GCD(72,52)
72 = 54 x 1 + 18 GCD(1260,198) = GCD(54,18)
54 = 18 x 3 + 0 GCD(1260,198) = 18

(a) Write a recursive implementation of the Euclidean GCD function:
int gcd(int a, int b);
[Hint: Note that when the remainder is zero, the divisor will be the GCD]
(b) Write a short program to test your GCD function with the following values:

1280,198
197,13
120,60

Which component acts as a platform on which application software runs

Many everyday occurrences can be represented as a binary bit. for example, a door is open or closed, the stove is on or off, and the fog is asleep or awake. could relationships be represented as a binary value? give example.

Now you’re on your own. include a short summary of this section with plots in your lab report. write a matlab script file to do steps (a) through (d) below. include a listing of the script file with your report. 1 the soundsc(xx,fs) function requires two arguments: the first one (xx) contains the vector of data to be played, the second argument (fs) is the sampling rate for playing the samples. in addition, soundsc(xx,fs) does automatic scaling and then calls sound(xx,fs) to actually play the signal. mcclellan, schafer, and yoder, dsp first, 2e, isbn 0-13-065562-7. prentice hall, upper saddle river, nj 07458. c 2015 pearson education, inc. 4 mcclellan, schafer and yoder, signal processing first. prentice hall, upper saddle river, new jersey, 2003. c 2003 prentice hall. (a) generate a time vector (tt) to cover a range of t that will exhibit approximately two cycles of the 4000 hz sinusoids defined in the next part, part (b). use a definition for tt similar to part 2.2(d). if we use t to denote the period of the sinusoids, define the starting time of the vector tt to be equal to t , and the ending time as ct . then the two cycles will include t d 0. finally, make sure that you have at least 25 samples per period of the sinusoidal wave. in other words, when you use the colon operator to define the time vector, make the increment small enough to generate 25 samples per period. (b) generate two 4000 hz sinusoids with arbitrary amplitude and time-shift. x1.t / d a1 cos.2