Question 1

What are bitwise operators used for?

Accepted Answer

Working with individual bits inside an integer, useful for flags packed into one int (each bit = one boolean option), hardware register reads/writes, color channel manipulation (R, G, B, A as separate bytes), network packet headers, file format parsing, cryptography (XOR is core to many ciphers), permission systems (Unix chmod, file mode bits), and optimization (multiplying by 2 = left shift by 1).

Question 2

What's the difference between AND, OR, and XOR?

Accepted Answer

AND: bit is 1 only if both inputs are 1. Used for masking, keep certain bits, clear others. OR: bit is 1 if either input is 1. Used for setting bits. XOR: bit is 1 if exactly one input is 1. Used for toggling bits, swapping values without a temp variable, and many crypto primitives. NOT: flip every bit. AND/OR/NOT form a complete logic basis; XOR adds a property (a XOR a = 0) that makes it special.

Question 3

What do left shift and right shift do?

Accepted Answer

Left shift (x << n) moves bits left by n positions, filling with zeros. Equivalent to multiplying by 2ⁿ. Right shift (x >> n) moves bits right by n positions. For unsigned integers, fills with zeros (logical shift). For signed integers, depends on language, JavaScript's >> preserves the sign bit (arithmetic shift); >>> always fills with zero (logical shift). Practical: shifting is much faster than multiplication/division on most hardware.

Question 4

Why does ~5 equal -6 instead of just 'invert the bits'?

Accepted Answer

NOT (~) flips every bit including the sign bit. In two's complement representation, 5 = ...00000101. Flipping every bit gives ...11111010, which is -6 in two's complement. The relationship: ~x == -x - 1 always. If you only wanted to invert the lower 8 bits, you'd mask: ~5 & 0xFF = 0xFA = 250. Without masking, the inversion includes all the high-order zero bits that JS pretends don't exist.

Question 5

What's a bitmask?

Accepted Answer

An integer used to extract or set specific bits in another integer. Example: 0b00001111 (= 15) masks the lower 4 bits. (x & 0x0F) extracts the lower nibble. (x | 0xF0) sets the upper nibble to 1s. (x ^ 0xFF) flips all 8 bits. Masks are central to packed flag systems (e.g., 'is item visible' = flags & VISIBLE_BIT) and to extracting fields from bit-packed data (RGBA colors, IP addresses).

Question 6

What integer sizes does JavaScript use?

Accepted Answer

JavaScript numbers are 64-bit floats. But bitwise operators internally convert to 32-bit signed integers, perform the operation, and convert back. So (2**31) | 0 is -2147483648 (the sign bit got set). For values above 32 bits, use BigInt, bitwise ops work on BigInt and have unlimited width. Many calculators (including this one) implicitly use 32-bit unsigned by default for clarity; switch modes if you need different widths.

Question 7

How is two's complement negative representation calculated?

Accepted Answer

Take the positive value, flip every bit, add 1. For +5 in 8 bits: 00000101. Flip: 11111010. Add 1: 11111011 = -5. The advantage: addition works the same for positive and negative values without special hardware. The high bit is the 'sign bit', when set, the value is negative. This means an 8-bit signed integer has range -128 to +127 (one more negative than positive). The bitwise calculator displays both signed and unsigned interpretations.

Question 8

Is my data sent anywhere?

Accepted Answer

No. Bitwise operations are pure arithmetic, JavaScript & / | / ^ / ~ operators applied to numbers in your browser. Inputs and outputs stay local.

Question 9

What standards does Bitwise Calculator validate against?

Accepted Answer

Bitwise Calculator checks compliance with IEEE 754 (32-bit integers for bitwise ops).

Question 10

What are the limitations of Bitwise Calculator?

Accepted Answer

JavaScript bitwise operations work on 32-bit signed integers only Does not support 64-bit BigInt bitwise operations Right shift is arithmetic (sign-preserving)

Operator	Name	Rule	Example (12 & 10)
&	AND	Both must be 1	8 (1100 & 1010 = 1000)
\|	OR	Either can be 1	14 (1100 \| 1010 = 1110)
^	XOR	Exactly one must be 1	6 (1100 ^ 1010 = 0110)
~	NOT	Flip all bits	~12 = -13 (in 2's Comp)

Bitwise Calculator

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What is Bitwise Calculator?

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Bitwise Calculator

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01 Logical Operator Truth Matrix

02 Logic Processing Pipeline

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