Step 1: Determine the UTF-8 encoding bit layout
The character ⅇ has the Unicode code point U+2147. In UTF-8, it is encoded using 3 bytes because its codepoint is in the range of
0x0800to0xffff.
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 thexare the payload bits.UTF-8 Encoding bit layout by codepoint range Codepoint Range Bytes Bit pattern Payload length U+0000 - U+007F 1 0xxxxxxx 7 bits U+0080 - U+07FF 2 110xxxxx 10xxxxxx 11 bits U+0800 - U+FFFF 3 1110xxxx 10xxxxxx 10xxxxxx 16 bits U+10000 - U+10FFFF 4 11110xxx 10xxxxxx 10xxxxxx 10xxxxxx 21 bits Step 2: Obtain the payload bits:
Convert the hexadecimal code point U+2147 to binary:
00100001 01000111. Those are the payload bits.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 10000101 10000111
DOUBLE-STRUCK ITALIC SMALL E·U+2147
ⅇ
Character Information
Code Point
U+2147
HEX
2147
Unicode Plane
Basic Multilingual Plane
Category
Lowercase Letter
Character Representations
Click elements to copy| Encoding | Hex | Binary |
|---|---|---|
| UTF8 | E2 85 87 | 11100010 10000101 10000111 |
| UTF16 (big Endian) | 21 47 | 00100001 01000111 |
| UTF16 (little Endian) | 47 21 | 01000111 00100001 |
| UTF32 (big Endian) | 00 00 21 47 | 00000000 00000000 00100001 01000111 |
| UTF32 (little Endian) | 47 21 00 00 | 01000111 00100001 00000000 00000000 |
HTML Entity
ⅇ
URI Encoded
%E2%85%87
Description
The Unicode character U+2147, known as the Double-struck Italic Small E, is a typographical symbol that holds significant importance in digital text. Its primary usage lies within mathematical notation, where it is employed to represent the 'esper' operator, which signifies an expectation value in quantum mechanics and wave function theory. This character is specifically utilized in equations and formulas to denote the expected or average value of a physical quantity, making it an essential tool for scientists and researchers dealing with quantum phenomena. The Double-struck Italic Small E is distinct from its single-struck counterpart due to its double-struck or 'sans serif' style, which gives it a bold appearance that sets it apart in text. This unique visual characteristic makes it easily identifiable and helps to avoid confusion with similar characters in digital text. Despite its specific role within mathematical notation, the Double-struck Italic Small E has managed to maintain a level of cultural significance due to its association with advanced scientific concepts and the ongoing exploration of quantum mechanics. In summary, the Unicode character U+2147, or the Double-struck Italic Small E, is a crucial symbol in digital text for representing expectation values in mathematical notation, particularly within the context of quantum mechanics. Its unique style and cultural significance make it an indispensable tool for scientists, researchers, and anyone delving into advanced scientific concepts.
How to type the ⅇ symbol on Windows
Hold Alt and type 8519 on the numpad. Or use Character Map.