Arithmetics for Computers (Number Systems
and Operations)
The table below shows the number when in
decimal, binary and hexadecimal.
Numeral systems conversion table
DECIMAL
BINARY
HEXADECIMAL
0
0000
0
1
0001
1
2
0010
2
3
0011
3
4
0100
4
5
0101
5
6
0110
6
7
0111
7
8
1000
8
9
1001
9
10
1010
A
11
1011
B
12
1100
C
13
1101
D
14
1110
E
15
1111
F
How to convert from binary to decimal
Convert binary 110011.11 to decimal:
The decimal number is equal to the sum of powers of 2 of the binary number's '1' digits place:
1
|
1
|
0
|
0
|
1
|
1
|
.
|
1
|
1
|
1^5
|
1^4
|
0^3
|
0^2
|
1^1
|
1^0
|
.
|
1^-1
|
1^-2
|
= (1x1^5 )+(1x1^4 )+( 1x1^1)+(1x1^0).(1x1^-1 )+(1x1^-2)
= 51.75 #
How to convert from hex to binary
Convert
each 4 binary digits to hex digit according to this table:
Bin:
|
0000
|
0001
|
0010
|
0011
|
0100
|
0101
|
0110
|
0111
|
Hex:
|
0
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
1000
|
1001
|
1010
|
1011
|
1100
|
1101
|
1110
|
1111
|
8
|
9
|
A
|
B
|
C
|
D
|
E
|
F
|
Example #1
à Convert (01001110)2 to
hex:
(0100)2 = (4)16
(1110)2 = (E)16
----------------------------------------
(01001110)2 = (4E)16
Example #2
àConvert
(0100101000000001)2 to hex:
(0100)2 =
(4)16
(1010)2 =
(A)16
(0000)2 =
(0)16
+ (0001)2 = (1)16
-----------------------------------------
(0100101000000001)2 = (4A01)16
#
How to convert from hex to decimal
Example #1
E7A9 in base 16 is equal to each digit multiplied with its
corresponding power of 16:
E7A916 =
E
|
7
|
A
|
9
|
14×163
|
7×162
|
10×161
|
9×160
|
57344
|
1792
|
160
|
9
|
Total
= 59305
~ameerah~
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