Number Bases and Integer Modes

Number Base Reference

Base	Name	Digits
2	Binary	`0–1`
8	Octal	`0–7`
10	Decimal	`0–9`
16	Hexadecimal	`0–9`, `A–F`

Prefixed Literals

Use prefixes to identify integer bases explicitly.

Prefix	Base	Example
`0b`	Binary	`0b1111`
`0o`	Octal	`0o17`
`0x`	Hexadecimal	`0xF`
None	Decimal by default	`15`

All four examples represent the decimal value 15.

Input Base Selector

The Input base selector provides:

Auto
Binary
Octal
Decimal
Hex

Auto Mode

Auto recognizes explicit 0x, 0b, and 0o prefixes and treats ordinary integers as decimal.

Explicit Input Bases

In Integer / Bitwise mode, selecting a base changes how unprefixed integer literals are interpreted.

For example:

Expression: 1010
Input base: Binary
Mode: Integer / Bitwise

The value represents decimal 10.

Explicit prefixes continue to identify their own bases.

Important Parsing Detail

The implementation converts unprefixed non-decimal integer literals through JavaScript parseInt() before converting to BigInt.

This can lose precision for very large values.

For large exact integer literals, prefer explicit 0x, 0b, or 0o prefixes, or decimal literals in Auto mode.

Primary Display Base

Choose the preferred result representation.

Option	Output
Decimal	Base 10
Binary	Base 2
Octal	Base 8
Hex	Base 16
Show all bases	Multiple representations

In Integer / Bitwise mode, the result area also shows the bit pattern.

Floating-Point vs Integer Mode

Capability	Floating-Point	Integer / Bitwise
Decimal fractions	Yes	No
Trigonometric functions	Yes	No
Logarithms	Yes	No
Fixed-width masking	No	Yes
Bitwise operators	No	Yes
BigInt arithmetic	No	Yes
Signed/unsigned interpretation	No	Yes

Bit Widths

Integer mode provides four selectable widths.

Width	Unsigned Range	Signed Range
8-bit	0 to 255	-128 to 127
16-bit	0 to 65,535	-32,768 to 32,767
32-bit	0 to 4,294,967,295	-2,147,483,648 to 2,147,483,647
64-bit	0 to 18,446,744,073,709,551,615	-9,223,372,036,854,775,808 to 9,223,372,036,854,775,807

Signed Integers

When Signed is enabled, Radix Quest interprets the result using two's complement.

For an 8-bit example:

Expression: 255
Bit width: 8
Signed: Enabled

Result:

-1

Binary:

1111 1111

Unsigned Integers

Disable Signed to interpret the same bit pattern as a nonnegative integer.

Expression: 255
Bit width: 8
Signed: Disabled

Result:

Fixed-Width Overflow

Integer results are masked to the selected bit width.

For example:

Mode: Integer / Bitwise
Bit width: 8
Signed: Disabled
Expression: 255+1

Result:

The mathematical result 256 exceeds the unsigned 8-bit range, so the stored result wraps to zero.

Negative Values

Negative values are represented using fixed-width two's complement.

Example:

Expression: -1
Bit width: 8

Underlying bit pattern:

1111 1111

The decimal display depends on the Signed setting.

Multi-Base Output

Select Show all bases to display:

Signed decimal
Unsigned decimal
Hexadecimal
Octal
Binary

The bit visualization groups digits into sets of four.

Example

For decimal 255 in 8-bit mode:

Hex: 0xFF
Oct: 0o377
Bin: 0b1111_1111
Bits: 1111 1111

Floating-Point Base Display

Floating-point mode can display other bases when the result is a safe integer.

For non-integer results, the implementation does not convert fractional digits into binary, octal, or hexadecimal representations.

Recommendations

Use Floating-point mode for general mathematics and scientific calculations.

Use Integer / Bitwise mode for binary arithmetic, bit masks, fixed-width representations, and programmer-oriented operations.

Important: BigInt provides exact integer arithmetic internally, but Radix Quest deliberately masks integer values to the selected width. It is not an unlimited-width integer calculator.