INVISIBLE PLUS·U+2064

Character Information

Code Point
U+2064
HEX
2064
Unicode Plane
Basic Multilingual Plane
Category
Format

Character Representations

Click elements to copy
EncodingHexBinary
UTF8
E2 81 A4
11100010 10000001 10100100
UTF16 (big Endian)
20 64
00100000 01100100
UTF16 (little Endian)
64 20
01100100 00100000
UTF32 (big Endian)
00 00 20 64
00000000 00000000 00100000 01100100
UTF32 (little Endian)
64 20 00 00
01100100 00100000 00000000 00000000
HTML Entity
⁤
URI Encoded
%E2%81%A4

Description

The Unicode character U+2064, known as the Invisible Plus, is a less common but essential glyph used primarily in mathematical expressions and digital text. This enigmatic symbol is often utilized in computer algebra systems, where it serves as an operator to perform addition without visibly altering the sequence of characters. As a result, U+2064 can be employed to construct complex mathematical equations or formulas that require an invisible calculation step, preserving the aesthetic and readability of the content. While its usage may not be widely recognized, the Invisible Plus is a testament to the versatility and functionality of Unicode in representing a wide array of characters, symbols, and concepts.

How to type the symbol on Windows

Hold Alt and type 8292 on the numpad. Or use Character Map.

  1. Step 1: Determine the UTF-8 encoding bit layout

    The character has the Unicode code point U+2064. In UTF-8, it is encoded using 3 bytes because its codepoint is in the range of 0x0800 to 0xffff.

    Therefore we know that the UTF-8 encoding will be done over 16 bits within the final 24 bits and that it will have the format: 1110xxxx 10xxxxxx 10xxxxxx
    Where the x are the payload bits.

    UTF-8 Encoding bit layout by codepoint range
    Codepoint RangeBytesBit patternPayload length
    U+0000 - U+007F10xxxxxxx7 bits
    U+0080 - U+07FF2110xxxxx 10xxxxxx11 bits
    U+0800 - U+FFFF31110xxxx 10xxxxxx 10xxxxxx16 bits
    U+10000 - U+10FFFF411110xxx 10xxxxxx 10xxxxxx 10xxxxxx21 bits
  2. Step 2: Obtain the payload bits:

    Convert the hexadecimal code point U+2064 to binary: 00100000 01100100. Those are the payload bits.

  3. Step 3: Fill in the bits to match the bit pattern:

    Obtain the final bytes by arranging the paylod bits to match the bit layout:
    11100010 10000001 10100100