LinkMAX HSA300 ADSL Ethernet Router User’s Guide
Appendix
B
. Binary Numbers
127
B
Binary Numbers
Binary Numbers
In everyday life, we use the decimal system of numbers. In decimal,
numbers are written using the ten digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and
9. Computers, however, do not use decimal. Instead, they use
binary
.
Definition
binary numbers
Binary numbers are numbers written using only the two digits 0
and 1, e.g., 110100.
Hint
Does "base ten" sound familiar? (Think grade school.) Base ten is
just another name for decimal. Similarly, base two is binary.
Just as each digit in a decimal number represents a multiple of 10
(1, 10, 100, 1000, 10,000, etc.), each digit in a binary number
represents a multiple of 2 (1, 2, 4, 8, 16, etc.). For example:
Decimal
Binary
1,000's 100's 10's 1's
8's 4's 2's 1's
-
- 1 3
=
1 1 0 1
Also, since binary uses only two digits to represent all numbers, a
binary number has more digits than the same number in decimal. In
the example above, you can see that the decimal number 13 is the
same as the binary number 1101 (8 + 4 + 1 = 13).
Bits and bytes
Computers handle binary numbers by grouping them into units of
distinct sizes. The smallest unit is called a
bit
, and the most
commonly used unit is called a
byte
.
Definition
bit and byte
A
bit
is a single binary digit, i.e., 0 or 1.
A
byte
is a group of eight consecutive bits (the number of bits can
vary with computers, but is almost always eight), e.g., 11011001.
The value of a byte ranges from 0 (00000000) to 255 (11111111).
The following shows the values of the eight digits in a byte along
with a sample value:
128's 64's 32's 16's 8's 4's 2's 1's
1 0 1 0 1 1 0 1
The decimal value of this byte is 173 (128 + 32 + 8 + 4 + 1 = 173).
