CalcOpenly
Português

Bitwise calculator (AND, OR, XOR, NOT and shifts)

Bitwise AND, OR, XOR, NOT, NAND, NOR, shifts and rotates on 8- to 64-bit integers, shown in decimal, hex and binary with a bit-by-bit grid.

Atualizado Exemplos verificados: 8

Decimal, or prefix with 0x, 0b or 0o. Negative numbers are stored in two's complement.
Experimentar
Resultado
Resultado: 72
Número inteiro; Ao mais próximo; empates afastando-se de zero
Hex
0x48
Binary
0100 1000
Octal
0o110
Bits set to 1
2

A AND B is 0x48 (0100 1000), which is 72 whether read as signed or unsigned; 2 of the 8 bits are 1.

8-bit AND

A
1
1
0
0
1
0
1
0
B
0
1
0
1
1
1
0
0
Result (AND)
0
1
0
0
1
0
0
0
Como é calculado S

  1. Write the inputs as 8-bit patterns

    A=1100 1010,B=0101 1100A = \texttt{1100\,1010},\quad B = \texttt{0101\,1100}

    Negative inputs are stored as 2⁸ = 256 minus their magnitude (two's complement).

  2. Apply AND bit by bit

    1100 1010∧ 0101 11000100 1000\begin{array}{rr}& \texttt{1100\,1010} \\ \land\ & \texttt{0101\,1100} \\ \hline & \texttt{0100\,1000}\end{array}

    Result bit is 1 only where both bits are 1.

  3. Read as unsigned

    ∑bi 2i=72\sum b_i\,2^i = 72

Sobre Bitwise calculator (AND, OR, XOR, NOT and shifts)

Bitwise operators work on each bit position separately: AND gives 1 only where both bits are 1, OR where either is, XOR where they differ, and NOT flips every bit. Shifts move the whole pattern left or right, filling with zeros, or with copies of the sign bit for an arithmetic right shift, and rotates carry the bits that fall off one end back in at the other. Every result is cut to the chosen width of 8, 16, 32 or 64 bits.

Programmers use it to build and test bit masks, flags, permissions and hardware registers. The default, 0xCA AND 0x5C in 8 bits, keeps only the bits the two share: 1100 1010 AND 0101 1100 = 0100 1000, which is 0x48 or 72. XOR of the same pair gives 0x96, which reads as 150 unsigned or −106 signed.

Negative inputs are stored in two's complement, so −1 in 16 bits is 0xFFFF.

Exemplos resolvidos

0xCA AND 0x5C (8-bit)

Operation
A AND B
A
0xCA
B
0x5C
Largura
8-bit
Read the result as
Unsigned
Resultado
72
Hex
0x48
Binary
0100 1000
Bits set to 1
2

Fonte de verificação: Python 3.8: 0xCA & 0x5C = 72 = 0x48, bin(72).count('1') = 2

XOR read as signed

Operation
A XOR B
A
0xCA
B
0x5C
Largura
8-bit
Read the result as
Signed
Resultado
-106
Hex
0x96
Same bits, other reading
150 as unsigned

Fonte de verificação: Python 3.8: 0xCA ^ 0x5C = 150; int.from_bytes(bytes([150]), 'big', signed=True) = -106

NOT 0 in 64 bits (edge)

Operation
NOT A
A
0
Largura
64-bit
Read the result as
Unsigned
Resultado
18446744073709551615
Hex
0xFFFFFFFFFFFFFFFF
Same bits, other reading
-1 as signed
Bits set to 1
64

Fonte de verificação: Python 3.8: ~0 & (2**64 - 1) = 18446744073709551615

Arithmetic shift right keeps the sign

Operation
Shift A right (arithmetic, copies the sign bit)
A
-128
Shift by (bits)
2
Largura
8-bit
Read the result as
Signed
Resultado
-32
Hex
0xE0

Fonte de verificação: Python 3.8: -128 >> 2 = -32 (Python's >> on ints is arithmetic); -32 & 0xFF = 0xE0

Perguntas

What does XOR do?

XOR (exclusive or) gives 1 where the two bits differ and 0 where they match, so 0xCA XOR 0x5C = 0x96. Two properties make it useful: x XOR x = 0, and applying the same key twice restores the original. That is why XOR toggles flags, computes parity and checksums, and appears in simple ciphers. C, Java, JavaScript and Python all write it as ^.

What is the difference between a logical and an arithmetic right shift?

A logical right shift fills the vacated top bits with 0, while an arithmetic shift copies the sign bit so negative numbers stay negative. In 8 bits, 0x80 shifted right by 2 logically is 0x20 (32), but −128 shifted right by 2 arithmetically is 0xE0 (−32), which is −128 ÷ 4. Java and JavaScript write >>> for logical and >> for arithmetic; in C, >> on a negative signed value is implementation-defined.

How does a bit mask work?

A mask is a number whose 1 bits pick the positions you care about. AND with the mask keeps those bits and clears the rest, OR sets them, XOR toggles them, and AND with NOT mask clears them. x AND 0x0F keeps the low 4 bits, and −1 AND 0x0F0F in 16 bits gives 0x0F0F = 3855, because −1 is all ones. To test bit n, check whether x AND (1 << n) is non-zero.

What does a left shift do to a number?

Shifting left by n multiplies an unsigned value by 2^n as long as no 1 bits are pushed past the top: 0x0F << 4 is 0xF0 = 240. Bits that move beyond the width are lost, so in 8 bits 0xFF << 4 is also 0xF0, not 4,080. In C, shifting by the full width or more is undefined behavior, and x86 masks the shift count to 5 bits for 32-bit operands and 6 bits for 64-bit ones.

What is popcount?

Popcount (population count, or Hamming weight) is the number of 1 bits in a value: 0x48 = 0100 1000 has 2, and NOT 0 in 64 bits has 64. x86 has a single POPCNT instruction for it, C++20 exposes it as std::popcount and Java as Integer.bitCount. It counts set flags and gives the Hamming distance between two values as popcount(a XOR b).

Qual é a precisão de “Bitwise calculator (AND, OR, XOR, NOT and shifts)”?

A precisão depende dos dados inseridos e das hipóteses do método. O cálculo decimal usa 50 algarismos significativos, mas estimativas, métodos numéricos e dados de origem podem ter menor precisão; o arredondamento exibido não elimina essas limitações. Exemplos resolvidos verificados com fontes independentes: 8. Por exemplo, “0xCA AND 0x5C (8-bit)” é verificado com Python 3.8: 0xCA & 0x5C = 72 = 0x48, bin(72).count('1') = 2.

De onde vem o método?

ISO/IEC 9899:2024 (C23) §6.5.7 bitwise shift operators and §6.5.10–6.5.12 bitwise AND, XOR, OR (draft N3096); Intel 64 and IA-32 Architectures Software Developer's Manual, Vol. 2 — SAL/SAR/SHL/SHR and ROL/ROR.

Sobre esta calculadora

unsigned=∑i=0w−1bi 2isigned=−bw−1 2w−1+∑i=0w−2bi 2i\begin{aligned} \text{unsigned} &= \sum_{i=0}^{w-1} b_i\,2^i \\ \text{signed} &= -b_{w-1}\,2^{w-1} + \sum_{i=0}^{w-2} b_i\,2^i\end{aligned}

Fontes

  1. ISO/IEC 9899:2024 (C23) §6.5.7 bitwise shift operators and §6.5.10–6.5.12 bitwise AND, XOR, OR (draft N3096)
  2. Intel 64 and IA-32 Architectures Software Developer's Manual, Vol. 2 — SAL/SAR/SHL/SHR and ROL/ROR

Verificado com as referências

Esta calculadora inclui 8 exemplos resolvidos com respostas de fontes independentes. Eles fazem parte do conjunto de testes e você também pode executá-los aqui.

Calculadoras relacionadas