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Array of bits

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• Bit arrays
  • Fact:

    The C programming language does not provide support for array of bits

    However:

    The C programming language provides all the necessary operations to allow the programmer (= you) to implement an "array of bits" data structure.

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• Implementing an array of bits
  • What is an array of bits:

    An array of bits A is an array where: A[i] = 0 or 1

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  • Trivial implementation:

    Use an array of int: int A[100]; // A[i] = 0 means false, A[i] = 1 means true Disadvantage: Each int variable is 32 bits We only need 1 bit to represent true/false We are wasting 31/32 (96.875%) of the memory space !!!

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  • An Efficient implementation of bit arrays:

    Use an array of int (because the most cost efficient access to memory is accessing int sized data): Map the bit array onto the array of integer as follows: Mapping function: Element with index k in the bit array is: bit position k % 32       in the array element with index k/32

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• Setting the k^th bit in array A
  • SetBit(A, k): set the k^th bit in the bit array A:

    Step-by-step: int i = k/32; // i = array index (use: A[i]) int pos = k%32; // pos = bit position in A[i] unsigned int flag = 1; // flag = 0000.....00001 flag = flag << pos; // flag = 0000...010...000 (shifted k positions) A[i] = A[i] | flag; // Set the bit at the k-th position in A[i]

    "Professional" version:

    SetBit( A[ ], k ): A[k/32] |= 1 << (k%32); // Set the bit at the k-th position in A[i]

    In C macro definition:

    #define SetBit(A,k) ( A[(k/32)] |= (1 << (k%32)) )

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• Clearing the k^th bit in array A
  • ClearBit(A, k): clear the k^th bit in the bit array A:

    Step-by-step: int i = k/32; int pos = k%32; unsigned int flag = 1; // flag = 0000.....00001 flag = flag << pos; // flag = 0000...010...000 (shifted k positions) flag = ~flag; // flag = 1111...101..111 A[i] = A[i] & flag; // RESET the bit at the k-th position in A[i]

    Pro version:

    ClearBit(A, k): A[k/32] &= ~(1 << (k%32));

    In C macro definition:

    #define ClearBit(A,k) ( A[(k/32)] &= ~(1 << (k%32)) )

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• Testing the k^th bit in array A
  • TestBit(A, k): test the k^th bit in the bit array A:

    Step-by-step: int i = k/32; int pos = k%32; unsigned int flag = 1; // flag = 0000.....00001 flag = flag << pos; // flag = 0000...010...000 (shifted k positions) if ( A[i] & flag ) // Test the bit at the k-th position in A[i] // k-th bit is 1 else // k-th bit is 0

    Pro version:

    TestBit( A, k ): if ( (A[k/32] & (1 << (k%32) )) != 0 ) // k-th bit is 1 else // k-th bit is 0 Or: if ( (A[k/32] & (1 << (k%32) )) ) // value != 0 is "true" in C ! // k-th bit is 1 else // k-th bit is 0

    In C macro definition:

    #define TestBit(A,k) ( A[(k/32)] & (1 << (k%32)) )

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  • Example Program: (Demo above code)                                                
    • The bit manipulation macros header file: click here
    • Test Prog file: click here

    How to run the program:

    Right click on link and save in a scratch directory To compile:   gcc bit-array2.c To run:          a.out