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by Aaron Patterson

Write a class that can represent a signed or unsigned number with an arbitrary
number of bits.  This class should support all bitwise operations ( & ^ ~ | ),
basic math operations ( + - / * ), and comparison operators.  It would behave
like an integer in C (except with arbitrary length!), so an unsigned int
0xFFFFFFFF + 1 would equal 0x00000000.

One edge case is what to do in an overflow case ( see the first irb session
number 2 ).  Another is how to handle numbers that are wider than the specified
number of bits.  I'm not really sure how to handle that part, but what I do is
just take the last N number of bits.  So if 0xFFEE was passed in to my 8 bit
vector, I would just take 0xEE.

Example irb sessions

Here is an example of using an 8 bit unsigned int with an initial value of 0xFF:

irb(main):001:0> n = UnsignedFixedWidthInt.new(0xFF, 8)
=> 255
irb(main):002:0> n += 2
=> 1
irb(main):003:0> n = n << 1
=> 2
irb(main):004:0> n = n >> 1
=> 1
irb(main):005:0> ~n
=> 254
irb(main):006:0> n += 12
=> 13
irb(main):007:0> n = n & 0x0E
=> 12
irb(main):008:0>

Now an example of an 8 bit signed int with an initial value of 0x01:

irb(main):001:0> n = SignedFixedWidthInt.new(0x01, 8)
=> 1
irb(main):002:0> n = n << 7
=> -128
irb(main):003:0> n -= 1
=> 127
irb(main):004:0> n = n >> 6
=> 1
irb(main):005:0> n -= 2
=> -1
irb(main):006:0> n = n ^ 0xF3
=> 12
irb(main):007:0> n = n | 0x01
=> 13
irb(main):008:0>

Here is an example of handling numbers that are too wide:

irb(main):001:0> n = UnsignedFixedWidthInt.new(0x0, 8)
=> 0
irb(main):002:0> n += 0xFFEE
=> 238
irb(main):003:0>

```