Code to concatenate two numbers' bits not working

Question

The task is to concat the binary of 2 given numbers.

Example:

Given 5 (101) and 3 (011),

Answer 1

Your problem is that you're feeding the bits of the second number in backwards. That's because x%2 is the low order bit:

+---+---+---+       <110
| 1 | 0 | 1 | <-----------------+^
+---+---+---+                   |1
              +---+---+---+     |1
              | 0 | 1 | 1 | ----+0
              +---+---+---+ 011>

Cringe at my awesome artistic abilities :-) However, if you already know that it's 3 bits wide, just use:

public class concat {
    public static void main (String[] args) {
        int t = 0;
        int k = 5;
        int x = 3;

        k <<= 3;
        k |= x;
        // or, in one line: k = (k << 3) | x;

        System.out.println(k);
    }
}

---

In terms of how that looks graphically:

                  +---+---+---+
                k:| 1 | 0 | 1 |
                  +---+---+---+
                  +---+---+---+
                x:| 0 | 1 | 1 |
                  +---+---+---+

      +---+---+---+---+---+---+
k<<=3:| 1 | 0 | 1 | 0 | 0 | 0 |
      +---+---+---+---+---+---+
                  +---+---+---+
                x:| 0 | 1 | 1 |
                  +---+---+---+

      +---+---+---+---+---+---+
 k|=3:| 1 | 0 | 1 | 0 | 1 | 1 |
      +---+---+---+---+---+---+
                    ^   ^   ^
                  +---+---+---+
                x:| 0 | 1 | 1 |
                  +---+---+---+

---

There's no apparent reason for doing it one bit at a time.

Answer 2

You just shift one number and then or with the other number:

int a = 5;
int b = 3;
int c = (a << 3) | b;

Answer 3

I don't know what language you are using, it's almost Java, so I am going with that.

This returns the result you are asking for, though you haven't given rules for determining how you know that 3 should be 011 instead of 11.

I have made the assumption that you want to assume that both numbers have the same number of bits, so 3 is 011 because 5 requires 3 bits.

public class Concat {
  public static void main(String[] args) {
    System.out.println( joinNums(3,5) );
  }

  public static int numBits( int n ) { 
    return (int)Math.ceil( Math.log(n) / Math.log(2) );
  }

  public static int joinNums( int num1 , int num2 ) {
    int bits = Math.max( numBits(num1) , numBits(num2) );
    return (num1 << bits) + num2;
  }
}