Bit Fiddling

This HW will give you a chance to practice using binary and bit-wise operators. You’ll likely find Booleans a useful reference.

Task

Visit https://kytos02.cs.virginia.edu/cso1/bitfiddle.php and complete the four problems listed below. The text boxes want lightweight code using just operators and assignments, like:

x = 0x20
y = b + x

That is, set x to be the hex value 0x20, then set y to be the value of b plus x.

The goal is to end up with one variable having a particular value, as defined in the instructions, based on other variables that are provided with new values in each test case. Do not add conditionals, loops, subroutines, etc.

The Tasks

We want you to do four of the problems. There are others puzzles on the site as well if you want more practice, but the only four we grade are:

isequal

Given x and y, set z to 1 if x == y; otherwise set z to 0 without using == or multi-bit constants.

For full credit, use ≤ 5 operations from {!, ~, +, <<, >>, &, ^, |} and up to 1-bit constants.

allevenbits

Given x, set y to 1 if all the even-numbered bits of x are set to 1 (where bit 0 is the least significant bit); otherwise set y to 0.

For full credit, use ≤ 12 operations from {!, ~, +, -, <<, >>, &, ^, |} and up to 8-bit constants.

bottom

Given b, set the low-order b bits of x to 1; the others to 0. For example, if b is 3, x should be 7. Pay special attention to the edge cases: if b is 32 x should be −1; if b is 0 x should be 0. Do not use - in your solution.

For full credit, use ≤ 40 operations from {!, ~, +, <<, >>, &, ^, |}.

bitcount

Given x, set y to the number of bits in x that are 1.

For full credit, use ≤ 40 operations from {!, ~, +, -, <<, >>, &, ^, |}.

Examples

We will do one example in class when we reach the HW1 material. However, if you’d like to practice beforehand, here is the description of subtract:

subtract (in-class example)

Given x and y, set z to x - y without using - or multi-bit constants.

For full credit, use ≤ 10 operations from {!, ~, +, <<, >>, &, ^, |}.

Collaboration

This Homework ONLY: You may work with other students in this class on this assignment, but only in the following two ways:

1. You worked together from the beginning, solving the problem as a team, with each person contributing.

   Each teammate should cite this in each problem with a C-style comment at the top of each solution and also cite the originator of any single-person contributions where they appear, like

    // Part of a team with mst3k and jh2jf 
    x = -y
    w = -x // jh2jf came up with this line
    z = x + y
   

2. You helped someone with a task you’d already finished, helping them think through their incorrect solution and not giving them or trying to lead them to your solution.

   The helper should acknowledge they did this by returning to their previously-submitted solutions and re-submitting them with an added comment at the top, like

    // I helped tj1a
    x = -y
    w = -x
   

   The helpee should acknowledge they got this by adding a comment at the top, like

    // tj1a helped me
    x = -y
    w = -x
   

In all cases, include computing IDs in your citations to streamline our automated tools that assist with collaboration checking.

Hints

If needed, we have some hints you can look at.

ans = 0;
for(int i=0; i<32; i+=1) {
    a += x&1;
    x >>=1;
}    

0b00e00h
0a00d00g
0000c00f