DecimalBinary
Converter
This program converts decimal numbers to binary.
The
binary system is a base two system. The only digits that can be used
are 0 and 1.
The first 17
decimal integers and their binary equivalents: 
Decimal 
Binary 
Decimal 
Binary 
0 
0 
9 
1001 
1 
1 
10 
1010 
2 
10 
11 
1011 
3 
11 
12 
1100 
4 
100 
13 
1101 
5 
101 
14 
1110 
6 
110 
15 
1111 
7 
111 
16 
10000 
8 
1000 


Positional Notation in the Binary Number System.
We saw that each digit in a decimal number carries its own weight. The rightmost digit in a decimal number is the units digit; the weight of each digit increases by a factor of 10 as one moves to the left.
Computers use binary number notation extensively. In computers, each digit in a binary number is called a bit. Eight bits make up one byte. The rightmost digit in a binary number is the units digit. The weight of each digit increases by a factor of 2 as one moves from right to left in a binary number. The following table gives the positional weight of each bit in the byte 1100 0101 and uses the positional weight of each column to express the number in decimal form:
5 Positional Weight 
2^{7} 
2^{6} 
2^{5} 
2^{4} 
2^{3} 
2^{2} 
2^{1} 
2^{0} 
Value 
128 
64 
32 
16 
8 
4 
2 
1 
Number 
1 
1 
0 
0 
0 
1 
0 
1 
Positional Notation 
1100 0101 =
1x128 + 1x64 + 0x32 + 0x16 + 0x8 + 1x4 + 0x2 + 1x1 = 197 
Note the LSD in 1100 0101 is the right most digit which is 1 and the MSD is the left most digit which is 1.
