What is the name of this 4-bit __pattern__: 1010 ?

A ― this is the name of the __pattern__ the four bits make.

4-bit Pattern Names

The
name of the binary pattern 1010 is "A".
The hex digit that
corresponds to the integer represented by 1010_{2} is also "A".

It is OK to have a pattern that has the name "A" and also to use "A" as a digit.

If a 4-bit pattern represents an integer in base two, that integer represented in base 16 is the same digit as the bit pattern name.

Base Sixteen Digits: | When describing Bit Patterns: | Hex digits in Binary |
---|---|---|

0 is a digit, representing zero. . . . A is a digit, representing ten. . . . F is a digit, representing fifteen. |
0 is the name of the pattern 0000 . . . A is the name of the pattern 1010 . . . F is the name of the pattern 1111 |
0 in 4-bit binary is 0000 . . . A in 4-bit binary is 1010 . . . F in 4-bit binary is 1111 |

The name of a 4-bit pattern (regarded as an abstract pattern) is the same as the hexadecimal digit whose representation in binary is that 4-bit pattern. This is not accidental.

Here is an integer represented in base two: 1011. What is the representation in base two of the number times sixteen?

Hint: remember that trick with appending zeros.