Question

For this assignment I can only use basic bitwise operators and no control structures, so I’ve come up with this code so far to convert sign-magnitude to two’s complement.

int sm2tc(int x) {
    // Invert and add 1
    // Problem: sm has 2 zeros.. 1000...000 & 0000...000
    int tmin = 1 << 31;
    int mask = x >> 31;  // Determine sign of x
    int mask2 = ~tmin; // Negate tmin to get 0111111...
    int first = (x ^ mask) + (~mask + 1) ;
    int second = first & mask2; // Turns of MSB
    return second;
}

Where have I gone wrong?

Answer 1

So, what you really want to compute is

result = (x & sign_bit) ? -(x & ~sign_bit) : x;

But of course you’re not allowed control structures. The first step is to rewrite -(x & ~sign_bit) using just the + and ^ operators: (-1 ^ (x & ~sign_bit)) - -1. Now note that if (x & sign_bit) is zero then (0 ^ (x & ~sign_bit)) - 0 is equal to x. We now have

result = (x & sign_bit) ? (-1 ^ (x & ~sign_bit)) - -1 : (0 ^ (x & ~sign_bit)) - 0

You then just need to replace the -1 and 0 with functions of x that generate those values depending on the sign bit, and lo and behold both sides of the condition become the same expression and the condition becomes unnecessary.