Question

This homework is an approach to generating random numbers. In this technique a seed value is used to construct a new (seemingly random) value in the following manner:

 The seed, s, is written down in n-bit binary.

 Several bit positions, called taps, are used to generate a feedback bit. Bit n-1 is always one of the taps.

 The feedback bit, f is the exclusive-or of the tap bit values

 The seed is shifted to the left one bit, dropping the leftmost bit. The rightmost bit is set to f.

In this manner, a seed is transformed into a new (hopefully different!) value which may be used for whatever purpose is desired. This value can also serve as the next seed. If the taps are picked appropriately, a large number of unique values (ideally 2n -1) are generated before the original seed reappears. (This technique has one obvious deficiency that will not concern us: a seed of 0 will generate 0 and lock up the mechanism.)

For example, using a nibble:

User inputs seed of 6= 0110

User enters the taps 3 and 2. (These are the bit numbers, remember that BIT n-1 is always used so bit 3 would be used even if the user did not enter it.)

0110 the feedback is bit3 xor bit2, f = 0 xor 1= 1

Shift the bits to the left dropping the leftmost bit and the rightmost bit is set to f, which equals one. 1101=13.

The random number is now 13.

If we looped with 13 now being the seed.

1 xor 1 = 0 1010=10.

10 would be the next random number.

Write a C program:

1. Use a command line argument for an unsigned integer for the seed and validate that this is a positive integer. End program if not a valid number. (Remember that it is a string and you must convert it to an integer.)

2. Prompt the user for the taps, end with a -1. Validate that the taps (bit numbers) are between 0 and 31. End the program if invalid.

3. Prompt the user for the number of random numbers that they would like to generate. Must be a positive integer greater than 0. If invalid ask user again to enter the number again.

4. Output the random numbers generated to a file “random.txt.”