Decimal number system
In a decimal number system, we have 10 digits, i.e., 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
A decimal number system has a base of ten (10). for example,
LSD = Least significant digit
MSD = Most significant digit
Binary number system
A number system which has only two digits, i.e. 0 (low) and 1 (high) is known as binary system. The base of binary number system is 2.
 Each digit in binary system is known as a bit and a group of bits is known as a byte.
 The electrical circuit which operates only in these two states i.e., 1 (on or high) and 0 (i.e., off or low) are known as digital circuits (Table 2).
Table 2 Different Names for the Digital Signals
State code

1

0

Name for the state

On

Off

Up

Down


Close

Open


Excited

Unexcited


True

False


Pulse

No pulse


High

Low


Yes

No

Decimal to binary conversion
 Divide the given decimal number by 2 and the successive quotients by 2 till the quotient becomes zero.
 The sequence of remainders obtained during divisions gives the binary equivalent of decimal number.
 The most significant digit (or bit) of the binary number so obtained is the last remainder and the least significant digit (or bit) is the first remainder obtained during the division.
2 
61 
Remainder 
2 
30 
1 LSD 
2 
15 
0 
2 
7 
1 
2 
3 
1 
2 
1 
1 

0 
1 MSD 
Binary to decimal conversion
The least significant digit in the binary number is the coefficient of 2 with power zero. As we move towards the left side of LSD, the power of 2 goes on increasing.
For example: (11111100101)_{2} = 1 Ã— 2^{10} + 1 Ã— 2^{9} + 1 Ã— 2^{8} + 1 Ã— 2^{7} + 1 Ã— 2^{6} + 1 Ã— 2^{5} + 0 Ã— 2^{4} + 0 Ã— 2^{3} + 1 Ã— 2^{2} + 0 Ã— 2^{1} + 1 Ã— 2^{0} = 2021