/* * getByte - Extract byte n from word x * Bytes numbered from 0 (LSB) to 3 (MSB) * Examples: getByte(0x12345678,1) = 0x56 * Legal ops: ! ~ & ^ | + << >> * Max ops: 6 * Rating: 2 */ int getByte(int x, int n) { return 0xff & (x >> (n << 3)); } /* * isNegative - return 1 if x < 0, return 0 otherwise * Example: isNegative(-1) = 1. * Legal ops: ! ~ & ^ | + << >> * Max ops: 6 * Rating: 2 */ int isNegative(int x) { x = x >> 31; return !!x; } /* * conditional - same as x ? y : z * Example: conditional(2,4,5) = 4 * Legal ops: ! ~ & ^ | + << >> * Max ops: 16 * Rating: 3 */ int conditional(int x, int y, int z) { int mask = (!x + ~0x00); return ((~mask) & z) | ((mask) & y); } /* * ezThreeFourths - multiplies by 3/4 rounding toward 0, * Should exactly duplicate effect of C expression (x*3/4), * including overflow behavior. * Examples: ezThreeFourths(11) = 8 * ezThreeFourths(-9) = -6 * ezThreeFourths(1073741824) = -268435456 (overflow) * Legal ops: ! ~ & ^ | + << >> * Max ops: 12 * Rating: 3 */ int ezThreeFourths(int x) { int masks; int Sign; int base; int Fourths; x = ((x << 1) + x); //multiply by 3 and then use pwrof2 masks = (1 << 2) + ~0; Sign = x >> 31; base = masks & Sign; Fourths = ((x + base) >> 2); return Fourths; } /* * isNonNegative - return 1 if x >= 0, return 0 otherwise * Example: isNonNegative(-1) = 0. isNonNegative(0) = 1. * Legal ops: ! ~ & ^ | + << >> * Max ops: 6 * Rating: 3 */ int isNonNegative(int x) { return !(x >> 31); } /* * isNonZero - Check whether x is nonzero using * the legal operators except ! * Examples: isNonZero(3) = 1, isNonZero(0) = 0 * Legal ops: ~ & ^ | + << >> * Max ops: 10 * Rating: 4 */

int isNonZero(int x) { return ((x | (~x + 1)) >> 31) & 1; }

explain what each code does, I have a general understanding but want to know more of how each works