Bits, binary, and bitwise operators

Numbers are bits

• Inside the computer, every int is a row of bits — each bit is a 0 or a 1.
• We usually read numbers in base 10, but the machine stores them in base 2 (binary).
• Bitwise operators let you look at and change individual bits.

Place value and powers of two

• In binary, each position is a power of two: 1, 2, 4, 8, 16, ...
• The byte 00010100 is 16 + 4 = 20. The rightmost bit is the 1s place.
• An 8-bit byte can hold 0 to 255.

Reading a bit with >> and & 1

• The shift n >> i moves the bits right by i places, so bit i lands in the 1s place.
• The mask & 1 keeps only that lowest bit, giving 0 or 1.
• So (n >> i) & 1 reads the value of bit number i.

The bitwise operators

• & (and), | (or), ^ (xor), ~ (not) combine numbers bit by bit.
• << and >> shift bits left or right. Shifting left by 1 doubles a number.
• These are the tools for masks, flags, and low-level tricks.

#include <stdio.h>

int main(void) {
    int n = 20;
    for (int i = 7; i >= 0; i--) {   // from the highest bit down
        printf("%d", (n >> i) & 1);
    }
    printf("\n");                    // 00010100
    return 0;
}

Common mistakes

• & is bitwise AND and && is logical AND — do not confuse them.
• << 1 doubles a value; >> 1 halves it.

Now you try

• Use (n >> i) & 1 to read bit i, and a loop to look at every bit.
• For count_bits and get_bit, the parameter is unsigned int. Do not write a main for those.