Bitwise NOT and One's Complement

Understanding Bitwise NOT (~)

NOT is a unary operator — it takes a single operand and flips every bit: 0 becomes 1, and 1 becomes 0. The result is called the one's complement of the original value.

Truth Table

A | ~A
--|----
0 |  1
1 |  0

Worked Example (8-bit)

  42     = 00101010
~42      = 11010101   (213 unsigned, -43 signed)

One's Complement vs. Two's Complement

In a signed integer system using two's complement (which virtually all modern CPUs use), the relationship between NOT and negation is:

~A = -(A + 1)

So ~42 = -43, ~0 = -1, and ~(-1) = 0. This identity is useful for:

• Computing -(A + 1) without addition
• Creating bitmasks: ~0 produces all 1s (0xFFFFFFFF in 32-bit)
• Inverting a mask: ~mask gives the complement mask for clearing bits

Practical Patterns

Clear bits with AND + NOT:

// Clear bit 3 of value
value = value & ~(1 << 3);

Create a mask for the upper N bits:

// Mask for upper 4 bits of a byte
const mask = ~0x0F & 0xFF;  // 0xF0

Width Sensitivity

The result of NOT depends on the bit width. ~42 in 8-bit is 213 (unsigned) or -43 (signed), but in 32-bit it is 4294967253 (unsigned) or still -43 (signed). Always be aware of your integer width when using NOT.