Converting hex number to binary number is very easy, it's almost
trivial. The only requirement is that you know the
equivalent binary value of each hexadecimal "digit" (0
to F); or if not, you must know how to convert them by hand. Below is
a table that show each hexadecimal digit with it's corresponding
binary number.
Note that every binary number on this table consists of four
digits. This is necessary because the maximum hexadecimal
digit value is F or 15, which translates to
four-digits-binary 1111.
| HEX |
BINARY |
| 0 |
0000 |
| 1 |
0001 |
| 2 |
0010 |
| 3 |
0011 |
| 4 |
0100 |
| 5 |
0101 |
| 6 |
0110 |
| 7 |
0111 |
| 8 |
1000 |
| 9 |
1001 |
| A |
1010 |
| B |
1011 |
| C |
1100 |
| D |
1101 |
| E |
1110 |
| F |
1111 |
(Technically, any trailing 0 at the beginning of a number doesn't
mean anything. So, binary 0010 is the same as binary 10, but
for conversion purpose, include the trailing 0s.)
To convert a hexadecimal number to binary. Just write
down the binary value of each hex digit.
Example 1:
To convert hexadecimal F8 to binary, write down the binary for F
first, then the binary for 8.
So, the answer is 11111000.
This seems too easy, and it is. Use a calculator to convince
yourself.
Another example:
Convert hex number 1A to binary.
So, the answer is 00011010. (Note: Once you got the
answer, you can ignore the zeros at the beginning, so this can be also written as 11010.)
More examples:
| hex |
D |
|
C |
|
C |
|
|
| bin |
1101 |
|
1100 |
|
1100 |
|
|
| |
|
|
|
|
|
|
|
| hex |
1 |
|
0 |
|
0 |
|
3 |
| bin |
0001 |
|
0000 |
|
0000 |
|
0011 |
| |
|
|
|
|
|
|
|
| hex |
F |
|
3 |
|
A |
|
2 |
| bin |
1111 |
|
0011 |
|
1010 |
|
0010 |
| |
|
|
|
|
|
|
|
Binary to Hex Example:
This time, let's assume we have a binary number that needs to be
converted to hex. For example, the binary number
11010. In this case because the number of digits is not a
multiple of 4, insert 0s at the beginning to make the number
multiple of four. So it becomes 00011010. We then separate each
four-digits pair and get their
corresponding hex values.
So, the answer is 1A.
Memorizing the Table?
I don't recommend memorizing the binary number of each hex
digit. Also, if
you don't know where those 0s and 1s comes from, it's easy to make
mistakes and not knowing it, or even forget. I recommend
that you know where they come from, and you won't have to worry much about
forgetting. For example, know that 4 is 2^2, so the binary
of 4 must be 0100. Why? Let's convert it
systematically:
| DIVISION |
RESULT |
REMAINDER |
| 4/2 |
2 |
0 |
| 2/2 |
1 |
0 |
| 1/2 |
0 |
1 |
The answer is the remainders being read backward, which is 100.
4 = (0)*2^3 + (1)*2^2 + (0)*2^1 + (0)*2^0
Realize that this is the only way the number 4 in binary can be
represented.
ANumber = (b1)*(2^3) + (b2)*(2^2) +
(b3)*(2^1) + (b4)*(2^0)
or
ANumber = (b1)*8 + (b2)*4 + (b3)*2 +
(b4)*1
where b1, b2, b3, b4 must be either 1 or
0.
So, let's say we're looking for the binary of 9. What
sequence of bs will sum to 9? There's always one
unique answer:
9 = (1)*8 + (0)*4 + (0)*2 + (1)*1
b1=1
b2=0
b3=0
b4=1
So the binary of 9 is 1001.
How about the binary of 7. What sequence of bs
will sum to 7? Again, there's only one answer:
7 = (0)*8 + (1)*4 + (1)*2 + (1)*1
b1=0
b2=1
b3=1
b4=1
So the binary of 7 is 0111.
I've added a decimal column to the table; it's shown
below. See Converting
Binary.
| HEX |
DECIMAL |
BINARY |
| 0 |
0 = 0+0+0+0 |
0000 |
| 1 |
1 = 0+0+0+1 |
0001 |
| 2 |
2 = 0+0+2+0 |
0010 |
| 3 |
3 = 0+0+2+1 |
0011 |
| 4 |
4 = 0+4+0+0 |
0100 |
| 5 |
5 = 0+4+0+1 |
0101 |
| 6 |
6 = 0+4+2+0 |
0110 |
| 7 |
7 = 0+4+2+1 |
0111 |
| 8 |
8 = 8+0+0+0 |
1000 |
| 9 |
9 = 8+0+0+1 |
1001 |
| A |
10 = 8+0+2+0 |
1010 |
| B |
11 = 8+0+2+1 |
1011 |
| C |
12 = 8+4+0+0 |
1100 |
| D |
13 = 8+4+0+1 |
1101 |
| E |
14 = 8+4+2+0 |
1110 |
| F |
15 = 8+4+2+1 |
1111 |
|
