Number
Systems
Table
for Use in Simple Conversions
|
Decimal |
Octal |
Binary |
Hexadecimal |
|
0 |
0 |
0000 |
0 |
|
1 |
1 |
0001 |
1 |
|
2 |
2 |
0010 |
2 |
|
3 |
3 |
0011 |
3 |
|
4 |
4 |
0100 |
4 |
|
5 |
5 |
0101 |
5 |
|
6 |
6 |
0110 |
6 |
|
7 |
7 |
0111 |
7 |
|
8 |
10 |
1000 |
8 |
|
9 |
11 |
1001 |
9 |
|
10 |
12 |
1010 |
A |
|
11 |
13 |
1011 |
B |
|
12 |
14 |
1100 |
C |
|
13 |
15 |
1101 |
D |
|
14 |
16 |
1110 |
E |
|
15 |
17 |
1111 |
F |
Conversions between
Octal, Binary & Hexadecimal Table Lookup Octal == Binary
== Hexadecimal 7658 ==
111 110 101 == 0001 1111 0101 == 1F516 111 110
101 0001 1111 0101 groups of three groups of four
Octal == Binary ==
Hexadecimal
Conversion
of Base 10 to Any Other Base
Successive
Division of the Base 10 Number by the Base Number of the Target Base
Collecting
the Remainders in Reverse Order to Form the Target Base Number, e.g.,
76810 =
_____8
8|768
8|96 0
8|12 0
1
4
76810 =
14008
Restatement:
Conversion of Decimal Number to Any Base n, i.e.,
Successive
Divisions of the Decimal Number by n, preserving the remainders
6510 = X5
5
| 65
5 |13 0
2 3
6510 = 2305
Conversion
of Any Base to Base 10
Polynomial
Expansion of the Number, i.e., Multiply the Coefficient by the Base Raised to
the Power of the Exponent, e.g.,
14008 =
_______10
14008 = 1*83 + 4*82 + 0*81
+ 0*80 = 83 + 4*82 = 82
* (8 + 4) = 64 * 12 = 76810
3 2 1 0 Indexes Base == 8
Conversion
of Any Base n Number to a Decimal (Base 10) Number
Polynomial Expansion
2305 = 2 3 0 5 =
2*52 + 3*51 +0*50 = 50 +
15 + 0 =
6510
2 1 0
Coefficient
* IndexBase + Coefficient * IndexBase
+ …
Addition
Base n (1) dump the bucket when it has n
stones in it;
(2) add one stone to the bucket on the left
n n n
Subtraction
“Take
Away”
When
bucket is empty for Base n
(1)
remove one stone from the bucket on the left
(2) place
n stones in the bucket that was empty
1
n
Primitive Symbols
1,
2, 3, … , A, B, C, … , etc.
Composite Symbols
143, AC9, 1011, 75, etc.