首先声明datalab本人未完成，有4道题目没有做出来。本文博客记录下自己的解析，以便以后回忆。如果能帮助到你就更好了，如果觉得本文没啥技术含量，也望多多包涵。

/* 
 * bitAnd - x&y using only ~ and | 
 *   Example: bitAnd(6, 5) = 4
 *   Legal ops: ~ |
 *   Max ops: 8
 *   Rating: 1
 */
int bitAnd(int x, int y) {
  return ~(~x | ~y);
}
/* 
 * 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) {
  int offsetValue = 0xff;
  int offsetIndex = n << 3;
  int value = (x & (offsetValue << offsetIndex)) >> offsetIndex;
  return value & offsetValue;
}
/* 
 * logicalShift - shift x to the right by n, using a logical shift
 *   Can assume that 0 <= n <= 31
 *   Examples: logicalShift(0x87654321,4) = 0x08765432
 *   Legal ops: ! ~ & ^ | + << >>
 *   Max ops: 20
 *   Rating: 3 
 */
int logicalShift(int x, int n) {
    int offset = 0x1 << 31;
    int offsetValue = ~(offset >> n << 1);  
    return (x >> n) & offsetValue;
}
/*
 * bitCount - returns count of number of 1's in word
 *   Examples: bitCount(5) = 2, bitCount(7) = 3
 *   Legal ops: ! ~ & ^ | + << >>
 *   Max ops: 40
 *   Rating: 4
 */
int bitCount(int x) {
    return 2;
}
/* 
 * bang - Compute !x without using !
 *   Examples: bang(3) = 0, bang(0) = 1
 *   Legal ops: ~ & ^ | + << >>
 *   Max ops: 12
 *   Rating: 4 
 */
int bang(int x) {   
    return 2;
}
/* 
 * tmin - return minimum two's complement integer 
 *   Legal ops: ! ~ & ^ | + << >>
 *   Max ops: 4
 *   Rating: 1
 */
int tmin(void) {
  return (0x1 << 31);
}
/* 
 * fitsBits - return 1 if x can be represented as an 
 *  n-bit, two's complement integer.
 *   1 <= n <= 32
 *   Examples: fitsBits(5,3) = 0, fitsBits(-4,3) = 1
 *   Legal ops: ! ~ & ^ | + << >>
 *   Max ops: 15
 *   Rating: 2
 */
int fitsBits(int x, int n) {
  int offsetValue = 0x1 << n;
  int addValue = (offsetValue >> 1) & (~offsetValue);//2^(n-1)
  int value1 = x + addValue;//x - {-[2^(n-1)]}
  int value2 = addValue + (~x);//[2^(n-1)-1] - x
  int maxValue = 0x1 << 31;
  return (n >> 5) | ((!(value1 & maxValue)) & (!(value2 & maxValue)));
}
/* 
 * divpwr2 - Compute x/(2^n), for 0 <= n <= 30
 *  Round toward zero
 *   Examples: divpwr2(15,1) = 7, divpwr2(-33,4) = -2
 *   Legal ops: ! ~ & ^ | + << >>
 *   Max ops: 15
 *   Rating: 2
 */
int divpwr2(int x, int n) {
  int maxValue = 0x1 << 31;
  int offsetValue = ~(0x1 << 31 >> (32 + ~n));
  int andValue = offsetValue & x;
  return (x >> n) + ((!!(x & maxValue)) & (!!(andValue)));
}
/* 
 * negate - return -x 
 *   Example: negate(1) = -1.
 *   Legal ops: ! ~ & ^ | + << >>
 *   Max ops: 5
 *   Rating: 2
 */
int negate(int x) {
  return ~x + 1;
}
/* 
 * isPositive - return 1 if x > 0, return 0 otherwise 
 *   Example: isPositive(-1) = 0.
 *   Legal ops: ! ~ & ^ | + << >>
 *   Max ops: 8
 *   Rating: 3
 */
int isPositive(int x) {
    return (!(x >> 31)) ^ (!x);
}
/* 
 * isLessOrEqual - if x <= y  then return 1, else return 0 
 *   Example: isLessOrEqual(4,5) = 1.
 *   Legal ops: ! ~ & ^ | + << >>
 *   Max ops: 24
 *   Rating: 3
 */
int isLessOrEqual(int x, int y) {
    int offsetValue = 0x1;
    int offsetIndex = 31;
    int offsetSign = offsetValue << offsetIndex;
    int signX = !(x & offsetSign);
    int signY = !(y & offsetSign);
    int value1 = ((!signX) & signY )^ 0x0;
    int value2 = (signX & (!signY)) ^ 0x1;
    int value3 = (!((y + ~x + 1) & offsetSign)) ^ 0x0;
    return value1 | (value2 & value3);
}
/*
 * ilog2