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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.
     
    For example: Binary equivalence of 61

2

61

Remainder

2

30

1 LSD

2

15

0

2

7

1

2

3

1

2

1

1

0

1 MSD

 
⇒ (61)10 = (111101)2

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 × 210 + 1 × 29 + 1 × 28 + 1 × 27 + 1 × 26 + 1 × 25 + 0 × 24 + 0 × 23 + 1 × 22 + 0 × 21 + 1 × 20 = 2021




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