Pointers (a)
In This Section:
Computer Number Systems
Bits and Bytes
Computers store information in bits, which are labeled 0 (empty) or 1 (full).
A set of 8 bits is called a byte, like this: 1010 0010
Each byte has an address, which is labeled with a hexadecimal number, like this: C7.
Decimal, Hexadecimal, and Binary Numbers
Decimal Numbers
When we learn to count, we use Decimal numbers (0-10). The Decimal number system is also called Base 10, since after the number 9, we add a 0 for 10.
Hexadecimal Numbers
The address (location) of a byte is given in Hexadecimal numbers (0-F). This number system is called Base 16, since after the number 9, we use A, B, C, D, E, and F. After F, we add a 0 for 10.
Binary Numbers
Computers store information as Binary numbers (0-1). This number system is also called Base 2, since after the number 1, we add a 0 for 10.
Here is a chart to help you understand these numbers:
| Decimal |
Hexadecimal |
Binary |
| 0 |
0 |
0000 0000 |
| 1 |
1 |
0000 0001 |
| 2 |
2 |
0000 0010 |
| 3 |
3 |
0000 0011 |
| 4 |
4 |
0000 0100 |
| 5 |
5 |
0000 0101 |
| 6 |
6 |
0000 0110 |
| 7 |
7 |
0000 0111 |
| 8 |
8 |
0000 1000 |
| 9 |
9 |
0000 1001 |
| 10 |
A |
0000 1010 |
| 11 |
B |
0000 1011 |
| 12 |
C |
0000 1100 |
| 13 |
D |
0000 1101 |
| 14 |
E |
0000 1110 |
| 15 |
F |
0000 1111 |
| 16 |
10 |
0001 0000 |
Converting Binary Numbers to Decimal
Let's convert the binary number 1001 1010 to a decimal number:
| Binary= |
1 |
0 |
0 |
1 |
1 |
0 |
1 |
0 |
|
|
x128 |
x64 |
x32 |
x16 |
x8 |
x4 |
x2 |
x1 |
|
|
= |
= |
= |
= |
= |
= |
= |
= |
Decimal |
|
128 |
+0 |
+0 |
+16 |
+8 |
+0 |
+2 |
+0 |
=154 |
This means that binary 1001 1010 = decimal 154.
Converting Hexadecimal to Decimal
Let's convert the hexadecimal number C7F8 to a decimal number:
| Hexadecimal= |
C |
7 |
F |
8 |
|
|
x4096 |
x256 |
x16 |
x1 |
|
|
= |
= |
= |
= |
Decimal |
|
49152 |
+1792 |
+240 |
+8 |
=51192 |
This means that hexadecimal C7F8 = 51192 decimal.
Converting Hexadecimal to Binary
Hexadecimal numbers usually begin with 0x, which we don't count when converting to binary. Let's convert the hexadecimal number OxA2D3 to a binary number:
| Hexadecimal= |
A |
2 |
D |
3 |
|
|
= |
= |
= |
= |
|
|
1010 |
0010 |
1101 |
0011 |
=Binary |
This means that hexadecimal 0xA2D3 = 1010 0010 1101 0011 binary.
