Int16 -32,768 to 32,767 Two’s Complement Exactly 16 Bits Signed Integer

Signed 16-Bit Integer Decoder

Hex Int16 to Binary Converter

Convert a hexadecimal 16-bit pattern to exact binary and decode its signed Int16 value. Patterns from 0000–7FFF represent 0 through 32,767, while 8000–FFFF represent -32,768 through -1 using two’s-complement encoding.

Signed Int16 decoding Exact 16-bit output Sign bit identified Signed decimal value

Hex → Int16 Binary

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HEX INT16 BIT PATTERN

Raw hex 0000–FFFF · optional 0x prefix · sign comes from bit 15 · no external + or − sign

INT16 BINARY SIGNED 16-BIT

1111111111111111

Hex: FFFF Sign bit: 1 Type: Int16

Signed decimal: -1

INT16 INTERPRETATION If bit 15 = 1, signed value = unsigned − 65,536

FFFF → 1111111111111111 · sign bit 1 · unsigned 65535 · 65535 − 65536 = -1

TRY:

Data Type Int16

Width 16 bits / 2 bytes

Positive Range 0000–7FFF

Negative Range 8000–FFFF

Encoding Two’s complement

Hex Int16 to Binary Converter

The Hex Int16 to Binary Converter converts a raw hexadecimal 16-bit pattern into exactly sixteen binary digits and interprets that pattern as a signed Int16 integer.

Standard Int16 values use two’s-complement encoding. Patterns from 0000 through 7FFF are non-negative, while patterns from 8000 through FFFF decode to negative signed values.

Example: hexadecimal FFFF converts to 1111111111111111. As an Int16 two’s-complement value, that pattern represents -1.

What Is Int16?

Int16 is a signed integer data type stored in exactly sixteen bits, or two bytes. Its standard two’s-complement range extends from -32,768 through 32,767.

Int16 width: 16 bits Storage: 2 bytes Minimum: 1000000000000000 = -32768 Maximum: 0111111111111111 = 32767

Hex Int16 Range

All four-digit hexadecimal patterns from 0000 through FFFF are valid raw 16-bit patterns, but their signed meanings depend on the most significant bit.

Hex Range	Binary Range	Int16 Meaning
0000–7FFF	0000000000000000–0111111111111111	0 to 32,767
8000–FFFF	1000000000000000–1111111111111111	-32,768 to -1

How to Convert Hex Int16 to Binary

First convert the four hexadecimal digits directly to sixteen binary bits. Then inspect bit 15, the most significant bit, to determine whether signed two’s-complement decoding is required.

Example: FFFE F → 1111 F → 1111 F → 1111 E → 1110 Binary: 1111111111111110 Unsigned pattern: 65534 Because sign bit = 1: 65534 − 65536 = -2

Hex Int16 Conversion Examples

Hex	Int16 Binary	Signed Decimal
0000	0000000000000000	0
0001	0000000000000001	1
00FF	0000000011111111	255
1234	0001001000110100	4660
7FFE	0111111111111110	32766
7FFF	0111111111111111	32767
8000	1000000000000000	-32768
8001	1000000000000001	-32767
FFFD	1111111111111101	-3
FFFE	1111111111111110	-2
FFFF	1111111111111111	-1

Example: FFFF Hex as Int16

FFFF → 1111111111111111 Sign bit: 1 Unsigned pattern: 65535 Signed value: 65535 − 65536 = -1

Example: 8000 Hex as Int16

8000 → 1000000000000000 Unsigned pattern: 32768 Signed value: 32768 − 65536 = -32768

8000 is the minimum representable Int16 value.

Example: 7FFF Hex as Int16

7FFF → 0111111111111111 Sign bit: 0 Int16 value: 32767

7FFF is the largest positive Int16 value.

How the Int16 Sign Bit Works

Bit 15 is the most significant bit of a sixteen-bit word. Under Int16 two’s-complement interpretation, it separates non-negative patterns from negative patterns.

Bit 15 = 0 → 0 through 32767 Bit 15 = 1 → -32768 through -1

Int16 Signed Value Formula

The conversion from a raw 16-bit pattern to signed decimal can be expressed with a simple formula.

Let U = unsigned 16-bit pattern value If U < 32768: Int16 = U If U ≥ 32768: Int16 = U − 65536

For example, FFFE is unsigned 65,534, so its Int16 value is 65,534 − 65,536 = -2.

Int16 vs UInt16

The binary patterns are identical, but their numerical interpretations differ once bit 15 becomes one.

Hex	Binary	UInt16	Int16
0000	0000000000000000	0	0
7FFF	0111111111111111	32767	32767
8000	1000000000000000	32768	-32768
8001	1000000000000001	32769	-32767
FFFE	1111111111111110	65534	-2
FFFF	1111111111111111	65535	-1

Why Int16 Stops at Positive 32767

The largest non-negative two’s-complement 16-bit pattern is 7FFF, where the sign bit is still zero.

7FFF = 0111111111111111 = 32767

The next raw pattern is 8000, which starts the negative half of the Int16 range.

Why There Is No Positive 32768 in Int16

Hexadecimal 8000 cannot mean positive 32,768 when interpreted as Int16 because the pattern 1000000000000000 is reserved for -32,768.

If you need 8000 to represent positive 32,768, use UInt16 interpretation instead.

Why the Output Always Contains 16 Bits

Int16 is a fixed-width type. Positive values that use fewer than sixteen significant bits still require zero padding on the left.

Hex	Minimal Binary	Int16 Binary	Signed Value
1	1	0000000000000001	1
A	1010	0000000000001010	10
FF	11111111	0000000011111111	255
7FFF	111111111111111	0111111111111111	32767

Raw Int16 Hex Uses No Minus Sign

This calculator expects the encoded hexadecimal bit pattern itself. Negative values are represented by patterns in the 8000–FFFF range.

Int16 -1: FFFF Int16 -2: FFFE Int16 -32768: 8000

Entering -FFFF would be a mathematical sign-and-magnitude expression, not a raw Int16 bit pattern.

Optional 0x Prefix

A programming-style 0x or 0X prefix is accepted.

0xFFFE → FFFE → 1111111111111110 → Int16 -2

Why Hex 10000 Is Invalid for Int16

Int16 contains only sixteen bits. Hexadecimal 10000 requires seventeen bits, so it cannot be represented as a single Int16 raw pattern.

FFFF = 1111111111111111 = 16 bits 10000 = 10000000000000000 = 17 bits Invalid Int16 pattern

Does Endianness Affect Int16 Decoding?

An Int16 value occupies two bytes, so byte order can matter when raw bytes are read from memory, files or protocols. This page assumes the hexadecimal word has already been written in the intended numeric order.

Input: FFFE Converted directly as: FFFE → 1111111111111110 → -2

The calculator does not automatically reverse FE FF into FF FE or perform any other endian transformation.

Common Uses for Int16 Values

Signed 16-bit sensor readings.
Audio PCM sample values.
Embedded-system variables.
Hardware register decoding.
Signed protocol fields.
Binary file analysis.
Firmware debugging.
Two-byte signed counters and measurements.
Reverse engineering raw data.
Two’s-complement programming exercises.

Common Hex Int16 Conversion Mistakes

Reading FFFF as 65,535 instead of Int16 -1.
Reading 8000 as positive 32,768 instead of -32,768.
Using UInt16 interpretation when the field is signed.
Adding an external minus sign to an already encoded pattern.
Trying to fit hexadecimal 10000 into sixteen bits.
Using one’s-complement rules instead of two’s complement.
Automatically reversing the two bytes.
Confusing raw binary conversion with signed numerical interpretation.

Hex Int16 to Binary Converter FAQs

What is Int16?

Int16 is a signed 16-bit integer type with a standard two’s-complement range from -32,768 through 32,767.

What is FFFF hex as Int16?

FFFF converts to 1111111111111111 and represents signed Int16 value -1.

What is FFFE hex as Int16?

FFFE converts to 1111111111111110 and represents -2.

What is 8000 hex as Int16?

8000 converts to 1000000000000000 and represents -32,768.

What is 7FFF hex as Int16?

7FFF converts to 0111111111111111 and represents positive 32,767.

Why is FFFF -1 instead of 65535?

Int16 uses signed two’s-complement interpretation. The unsigned pattern is 65,535, and 65,535 – 65,536 equals -1.

Why does 8000 equal -32768?

Its unsigned raw value is 32,768. Since the sign bit is 1, Int16 decoding uses 32,768 – 65,536 = -32,768.

Can Int16 represent positive 32768?

No. The largest positive Int16 value is 32,767. Use UInt16 or a wider signed type for positive 32,768.

Can I enter -1 directly?

No. This converter expects a raw hexadecimal Int16 bit pattern. The encoded Int16 representation of -1 is FFFF.

Can I enter 0xFFFF?

Yes. One optional 0x or 0X prefix is accepted.

Can I enter hex 10000?

No. Hexadecimal 10000 requires 17 bits and does not fit inside Int16.

Does the converter reverse byte order?

No. The hexadecimal word is interpreted exactly in the order entered. Endian conversion is a separate operation.

Convert Hex to Int16 Binary

Enter a raw hexadecimal word from 0000 through FFFF and select Convert Hex Int16. The calculator converts the word to exactly sixteen binary digits, checks the most significant sign bit and returns the correct signed two’s-complement decimal value from -32,768 through 32,767.