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Bit Operators

Advanced — bonus activity

This page is only needed for the LED Speedometer bonus activity. If you are working through Labs 1–4, you can skip it for now.

Binary and bits

Every number stored in a computer is represented in binary — a sequence of 1s and 0s. Each digit is called a bit.

For example, the decimal number 13 in binary is 1101:

Bit position 3 2 1 0
Value 1 1 0 1
Place value (2ⁿ) 8 4 2 1

8 + 4 + 0 + 1 = 13. Each position is worth a power of 2.

Bit operators

Left shift <<

int x = 1 << 3;   // x == 8

<< shifts the bits of the left operand to the left by the number of positions given on the right. Shifting left by N is the same as multiplying by 2ⁿ.

1 in binary is 0001. Shift it left 3 → 1000 = 8.

Right shift >>

int x = 16 >> 2;  // x == 4

Shifts bits to the right. Shifting right by N is the same as dividing by 2ⁿ (integer division).

Bitwise AND &

int x = 13 & 4;   // x == 4

Compares each bit position. The result bit is 1 only if both input bits are 1.

  1101   (13)
& 0100   (4)
------
  0100   (4)

This is useful for reading a specific bit: (value & (1 << n)) is non-zero if bit N is set, zero if it is not.

Bitwise OR |

int x = 9 | 4;    // x == 13

The result bit is 1 if either input bit is 1.

  1001   (9)
| 0100   (4)
------
  1101   (13)

Reading bit N of a number

To check whether bit N of a value is 1:

if (value & (1 << n)) {
    // bit n is set
}

This is the pattern used in the binary LED speedometer approach — each LED corresponds to one bit of the speed value.

Try it

Pick a number between 0 and 31. Write it out in binary (5 bits). Which bits are set? Verify using the & and << operators in your program by printing the result.

See also