1011 0000. Appending four zeros multiplies the number being represented by 2^{4}.

Convert a hexadecimal representation of an integer into an unsigned binary representation directly by replacing each hex digit with its 4-bit binary equivalent. For example:

1 A 4 4 D (Hex Representation) 0001 1010 0100 0100 1101 (Binary Representation)

Recall that:

- (In base two) Shifting left by four bits is equivalent to multiplication by sixteen.
- (In base sixteen) Shifting left by one digit is equivalent to multiplication by sixteen.

To see how this works, look at this integer represented in base two and in base sixteen:

base two base sixteen 1010 = A

Now multiply each by sixteen:

base two base sixteen 1010 0000 = A0

Groups of four bits (starting from the right) match powers of sixteen, so each group of four bits matches a digit of the hexadecimal representation. Let us rewrite the integer C6D in binary:

C6D = C × sixteen^{2}+ 6 × sixteen^{1 }+ D × sixteen^{0 }= C × (2^{4})^{2}+ 6 × (2^{4})^{1}+ D × (2^{4})^{0}= 1100 × (2^{4})^{2}+ 0110 × (2^{4})^{1}+ 1101 × (2^{4})^{0}= 1100 × 2^{8}+ 0110 × 2^{4}+ 1101 × 1

Using the idea that each multiplication by two is equivalent to appending a zero to the right, this is:

= 1100 0000 0000 + 0110 0000 + 1101 C6D = 1100 0110 1101

Each
digit of hex can be converted into a 4-bit binary number,
each place of a hex number stands for a power of 2^{4}.
It stands for a number of 4-bit left shifts.

What is the name of the binary __pattern__ 0001 1010 0100 0100 1101 ?