1011 0000. Appending four zeros multiplies the number being represented by 24.

# Converting Hex Representation into Binary Representation

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 × sixteen2 +    6 × sixteen1   +    D × sixteen0

=    C × (24)2    +    6 × (24)1      +    D × (24)0

= 1100 × (24)2    + 0110 × (24)1      + 1101 × (24)0

= 1100 ×  28      + 0110 ×  24        + 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 24. It stands for a number of 4-bit left shifts.

### QUESTION 13:

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