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Shift operators: << and >>

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• The left shift shift operator of C
  • Left shift

    x << n = left shift the bit pattern x over n positions The right-most bit positions will be filled with 0 bits

    Example:

    char a = 0b00000001; char b = a << 1; /* b = 00000010 */ char c = a << 2; /* c = 00000100 */

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• The right shift shift operator of C
  • Right shift

    x >> n = right shift the bit pattern x over n positions Filler bit used: If the type of the variable x is an unsigned type: The left-most bit positions will always be filled with 0 bits If the type of the variable x is an signed type: The left-most bit positions will be filled with 0 bits if the left-most bit of x is equal to 0 The left-most bit positions will be filled with 1 bits if the left-most bit of x is equal to 1

    Example 1: unsigned type

    unsigned char a = 0b00000100; unsigned char b = 0b10000100; char c; c = a >> 1; /* c = 00000010 */ c = b >> 1; /* c = 01000010 */

    Example 2: signed type

    char a = 0b00000100; char b = 0b10000100; char c; c = a >> 1; /* c = 00000010 */ c = b >> 1; /* c = 11000010 */

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  • Example Program: (Demo above code)                                                
    • Prog file: click here

    How to run the program:

    Right click on link and save in a scratch directory To compile:   gcc shift1.c To run:          ./a.out

    Delete the unsigned keyword, re-compile it and re-run it !!!

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• Using the shift operators
  • Common usage of the shift operators

    Shift left one bit = multiply a value by 2 Example: Bit pattern | Value in decimal Left shift 1 bit | Value in decimal --------------+-------------------- -------------------+------------------- 00000011 | 3 00000110 | 6 00000101 | 5 00001010 | 10 Shift right one bit = divide a value by 2 (= quotient of a division by 2) Example: Bit pattern | Value in decimal Right shift 1 bit | Value in decimal --------------+-------------------- --------------------+------------------ 00000110 | 6 00000011 | 3 (= 6%2) 00000011 | 3 00000001 | 1 (= 3%2) 00000101 | 5 00000010 | 2 (= 5%2)

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  • Example C program:

    int main( int argc, char* argv[] ) { char a = 1; /* a = 00000001 (= 1) */ a = a << 1; /* Now: a = 00000010 (= 2) */ printf( "a = %d\n", a ); a = a << 1; /* Now: a = 00000100 (= 4) */ printf( "a = %d\n", a ); a = a >> 1; /* Now: a = 00000010 (= 2) */ printf( "a = %d\n", a ); a = a >> 1; /* Now: a = 00000001 (= 1) */ printf( "a = %d\n", a ); a = a >> 1; /* Now: a = 00000001 (= 0) */ printf( "a = %d\n", a ); }

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  • Example Program: (Demo above code)                                                
    • Prog file: click here

    How to run the program:

    Right click on link and save in a scratch directory To compile:   gcc mult-div1.c To run:          ./a.out

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• Example using shift operation: print an int variable in bit representation
  • Recall that int (integer) typed variables use the binary number system to represent values

    Examples:

    What is stored in an int variable | Value that is represented --------------------------------------+------------------------------- 00000000 00000000 00000000 00000000 | 0 00000000 00000000 00000000 00000001 | 1 00000000 00000000 00000000 00000010 | 2 00000000 00000000 00000000 00000011 | 3 .... ...

    In other words:

    When you write the following assignment statement: int x; x = 3; the computer will store the following bit pattern in the variable x: 00000000 00000000 00000000 00000011

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  • Problem description:

    Write an algorithm to print the bit pattern stored inside an int variable a (in binary format)

    Pseudo code:

    bit position 31 bit position 0 | | v v a = xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (32 bits) ^ | bit position i for ( i = 31; i >= 0; i-- ) if ( bit at position i in variable a == 1 ) print '1'; else print '0';

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  • C program:

    void printBits( int a ) { int i; /* 10987654321098765432109876543210 */ unsigned int mask = 0b10000000000000000000000000000000; for ( i = 31; i >= 0; i-- ) { if ( (a & mask) != 0 ) putchar('1'); else putchar('0'); mask = mask >> 1; /* Shift mask bit to right */ } }

    Note:

    I have written the algorithm as a C function Yes, I know that we have not covered C functions yet, but the syntax of C functions is very similar to that of Java (but without the class construct around it) The putchar(x) function will print the character x to the standard output (terminal).

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  • Whole C program:

    void printBits( int a ) { int i; /* 10987654321098765432109876543210 */ unsigned int mask = 0b10000000000000000000000000000000; for ( i = 31; i >= 0; i-- ) { if ( (a & mask) != 0 ) putchar('1'); else putchar('0'); mask = mask >> 1; /* Shift mask bit to right */ } } int main( int argc, char* argv[] ) { int a; printf( "a = " ); scanf( "%d", &a ); printf( "a = %d\n", a ); printf( "Binary representation = " ); printBits( a ); /* Call the printBits() function */ putchar('\n'); }

    Remember that: a C program always starts running in the main() function (just like Java)

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  • Example Program: (Demo above code)                                                
    • Prog file: click here

    How to run the program:

    Right click on link and save in a scratch directory To compile:   gcc pr-bits.c To run:          ./a.out

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• Final note
  • These shift operators are also defined in Java.

  • They are often omitted in introduction courses because they are not used in program at the introduction level.