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EXAMPLE CONVERSION - HEX TO DECIMAL
|
Hex |
Decimal Equivalent |
|
9AC3 |
39,619 |
|
Hex=Decimal
|
Comment |
Hexadecimal number to be
converted |
Decimal Equivalent |
|
0=0
1=1
2=2
3=3
4=4
5=5
6=6
7=7
8=8
9=9
A=10
B=11
C=12
D=13
E=14
F=15 |
Columns are numbered from right to left,
starting at column zero, not column one |
column 3 |
column 2 |
column 1 |
column 0 |
|
|
Write the hex number with one digit per
column |
9 |
A |
C |
3 |
|
|
Convert the hex digit to decimal |
9 |
10 |
12 |
3 |
|
|
Multiply each digit by 16 to the power of n,
where n is the column number |
9 x (16^3) |
10 x (16^2) |
12 x (16^1) |
3 x (16^0) |
|
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Put the answer in this row, and add all the
answers together |
36,864 |
+ 2,560 |
+ 192 |
+ 3 |
= 39,619 |
Definitions:
16^3 = 16 to the power of 3 = (16 x 16 x 16) = 4,096
16^0 = 16 to the power of 0 = 1 (anything to the power of zero
equals one.)
Explanation:
Each hex digit is multiplied by 16^n, where n is its column number,
numbering from right to left, starting at column zero (not
column 1).
Then all the answers are added together. This gives you the decimal
equivalent of the hex number you started with.
A general formula can be derived for those familiar with
mathematical notation:
Decimal Equiavalent = Σ (Hn x 16^n) from n = 0 to n
where Σ means "sum", n is the column number, and Hn is the hex digit
in the n-th column
EXAMPLE CONVERSION - HEX TO BINARY
|
Hex |
Binary Equivalent |
|
9AC3 |
1001 1010 1100 0011 |
|
Hex=Binary
|
Comment |
Hexadecimal number to be
converted |
Binary Equivalent |
|
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 |
Hex is directly related to binary and the
order of conversion does not matter. You can start at column 3
or column zero. |
column 3 |
column 2 |
column 1 |
column 0 |
|
|
Write the hex number with one digit per
column |
9 |
A |
C |
3 |
|
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Convert each hex number directly into binary
|
1001 |
1010 |
1100 |
0011 |
|
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The usual use of binary is in computers
where the binary digits are called bits and are grouped by 8's
to make one byte (one byte = 8 bits) |
1001 1010 |
1100 0011 |
1001 1010 1100 0011 |
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