Programmer Calculator: Hex, Binary and Bitwise Operations

What it is and when to use it

The programmer calculator works on machine integers: it shows one value in hexadecimal, decimal, octal and binary at once, and applies the bitwise operators AND, OR, XOR, NOT, NAND, NOR, shifts (<<, >>) and rotates (ROL, ROR). Values are held in a 64-bit QWORD, 32-bit DWORD, 16-bit WORD or 8-bit BYTE.

It fits register dumps, bitmasks, subnet masks, colour channels and file permission bits. It is integer-only: there is no decimal point, and division returns a whole-number quotient. Decimal arithmetic and percentages belong to the standard calculator, functions to the scientific calculator, plotted relationships to the graphing calculator.

Keys and inputs

Base rows.The four rows show the value in HEX, DEC, OCT and BIN. Clicking one converts the value and sets the base you type in.
Typing rules.Digits the active base lacks are unavailable: in BIN, 2–9 and A–F are disabled; in OCT, 8, 9 and A–F. Hexadecimal letters are active in HEX. A disallowed keystroke is ignored, with no error.
Word size.QWORD, DWORD, WORD and BYTE select 64, 32, 16 or 8 bits; the BIN row is padded to the full word.
Bit grid.Every bit is a button that flips it. In BYTE, setting the top bit shows 80 in HEX and -128 in DEC.
Operators.AND, OR, XOR, NAND, NOR, <<, >>, ROL and ROR wait for a second operand, like +, −, × and ÷. NOT applies immediately. % is integer modulo, not percent.
Keyboard.Digits and A–F type numbers (lower case works); + - * / % are arithmetic; & | ^ are AND, OR, XOR; < and > are shifts; ~ is NOT; Enter or = evaluates; Backspace deletes a digit and Esc clears. NAND, NOR, ROL and ROR have no shortcut. The clear key is labelled C, and HEX has a separate C digit key.

Worked examples

Pack a colour. With HEX active, 12 << 10 = shows 120000; OR 3400 = shows 123400; OR 56 = shows 123456, the 24-bit value of colour #123456, read as 1193046 in DEC.
Read a subnet mask. With DWORD and HEX active, C0A80407 AND FFFFFF00 = shows C0A80400 — the host bits cleared. The DEC row reads -1062730752 because bit 31 is set; change the word size to QWORD and the same C0A80400 reads 3232236544. The bits did not change, only the signed reading.
Shift a negative byte. With BYTE and HEX active, FF >> 1 = shows 7F, read as 127 in DEC. An arithmetic right shift would keep the -1 reading; this >> is logical and fills the vacated bit with 0.

Background

One hex digit is exactly four bits, so a byte is two digits and a 32-bit word is eight; that is why addresses, colour codes and network masks are read in hexadecimal. Two's complement, the signed convention in current CPUs, gives negative numbers a single zero and lets addition and subtraction share one circuit; the top bit carries the sign. A logical shift fills the vacated bit with zero, while the arithmetic shift used in compiled languages for signed types copies the sign bit instead.

Reading results, and the limits

Signed decimal, unsigned bases.: The DEC reading is signed two's complement for the selected word; HEX, OCT and BIN are those bits read unsigned: in BYTE, FF reads -1, but the same FF in QWORD reads 255, and 8000000000000000 reads -9223372036854775808. The main display spaces decimal digits in groups of three; the BIN row always shows the whole word in groups of four bits, while HEX and OCT print without leading zeros.
Truncation.: +, − and × compute an exact integer and then cut it to the word. When the raw result does not fit, the display shows the low bits with a note: in BYTE, 200 + 100 = shows 44 with Result 300 exceeds BYTE; truncated to 44, and 0 − 1 = shows -1 with Result -1 exceeds BYTE; truncated to 255. Shifts do not warn: a byte 80 shifted left by one gives 0, because the set bit leaves the word.
Division and modulo.: Division truncates toward zero. Enter F9 in HEX with BYTE selected: the DEC row reads -7, and ÷ 2 = shows -3. % keeps the sign of the left operand, so -7 % 3 = shows -1. Division or modulo by zero stops with Division by zero or Modulo by zero until C clears it.
Word size.: A literal bigger than the word stays on the display while the base rows show the masked value; the next operation cuts it and reports the truncation. Changing word size cuts the current value to the low bits: 256, then BYTE, shows 0.
Integers only.: It does not do decimal or floating-point arithmetic — there is no decimal point, and division returns a whole-number quotient; fractions and percentages belong to the standard calculator.

Common mistakes

Shift right is logical, not arithmetic. In BYTE, FF reads -1, yet >> 1 gives 7F (127) — a plausible-looking, wrong number for anyone expecting sign extension.
Reading DEC without checking the word size: FF is -1 in BYTE and 255 in QWORD.
Typing operands without watching the active base: with HEX active, 10 is 16 and 16 is 22.
Expecting fractions: 7 ÷ 2 = shows 3; the remainder is 7 % 2 =, which shows 1.
Expecting << to report bits that fall out: in BYTE, 80 << 1 gives 0 silently; only +, − and × report truncation.
Reaching for % as the percent key: here it is modulo; percent lives in the standard calculator.

Where it is used

Register and flag values. Flip single bits in the grid and read the same word as signed decimal, hex and octal while debugging masks.
Addresses and subnet masks. C0A80407 AND FFFFFF00 = clears the host bits to C0A80400 for a network range.
Colour channels. Pack RR GG BB bytes into 123456 with << and OR for 24-bit colour codes.
File permission bits. Set mode bits one by one and read the resulting number in OCT for chmod-style values.

Privacy

Every calculation runs in the browser. Nothing you type or compute is uploaded, and the page keeps no record of it.

Sources

MDN Web Docs, Bitwise AND (&) （访问日期：2026-09-30）— operand semantics over two's complement bit patterns.
Wikipedia, Bitwise operation （访问日期：2026-09-30）— AND, OR, XOR and NOT definitions.
Wikipedia, Logical shift （访问日期：2026-09-30）— zero-fill behaviour versus the sign-preserving arithmetic shift.
Wikipedia, Two's complement （访问日期：2026-09-30）— signed interpretation of a fixed-width word.
Wikipedia, Hexadecimal （访问日期：2026-09-30）— four bits per hex digit.

Sources & review

Reviewed by: CalcX Editorial Team
Updated: 2026-09-30