THE BINARY
NUMBER SYSTEM
“There are only 10 types of
people in this world:
Those who understand BINARY
and those who do not.”
IT’S ALL ONES AND ZEROS …
- Computers speak in a
language, very much like we
speak in English. We call it
binary code.
- This language consists of two
“letters”: 0 and 1
BINARY VERSUS DECIMAL NOTATION
- We are used to seeing numbers in the decimal notation, for
example: 143
- In decimal notation, we use digits from 0 to 9
- Each digit holds a value, which is some sequential power of 10
Let’s take a look:
143 = (1 x 100) + (4 x 10) + (3 x 1)
Which can also be written as …
143 = (1 x 102 ) + (4 x 101 ) + (3 x 100 )
BINARY VERSUS DECIMAL NOTATION
-
In the binary system, we use only two digits: 0 and 1
A single 0 or 1 is called a “bit”
A group of 8 bits is called a “byte” ex: 0100 1101
One byte has the possibility of 256 different values
Each digit holds a value, which is some sequential power of 2
BINARY VERSUS DECIMAL NOTATION
Let’s take a look at a few examples:
Decimal
Binary
2
10
5
101
38
100110
143
10001111
2 = 1 × 2 + (0 × 1)
2 = 1 × 21 + (0 × 20 )
5 = 1 × 4 + 0 × 2 + (1 × 1)
5 = 1 × 22 + 0 × 21 + (1 × 20 )
38 = (1 × 32) + 0 × 16 + 0 × 8 + 1 × 4 + 1 × 2 + 0 × 1
38 = (1 × 25 ) + 0 × 24 + 0 × 23 + 1 × 22 + 1 × 21 + 0 × 20
BINARY VERSUS DECIMAL NOTATION
Decimal
64
32
16
8
4
2
1
2
Binary 128
(Byte)
0000 0010 0
0
0
0
0
0
1
0
5
0000 0101
0
0
0
0
0
1
0
1
38
0010 0110
0
0
1
0
0
1
1
0
143
1000 1111
1
0
0
0
1
1
1
1
TRY THIS …
1. Write these numbers out in binary form:
a) 9
b) 22
c) 237
2. Convert these binary numbers into decimal notation:
a) 111
b) 101011
c) 10101111
ANSWERS
1. Write these numbers out in binary form:
a) 9
1001
b) 22
10110
c) 237
11101101
2. Convert these binary numbers into decimal notation:
a) 111
7
b) 101011
43
c) 10101111
175
ASCII
JUST FOR FUN …