Binary Number System:


The binary number system is a system of numbers to base 2, which uses the combination of the digits 1 and 0. Codes based on binary numbers are used to represent instructions and data in all modern digital computers. The values of binary digits are being stored or transmitted as open/Closed switches, magnetized/magnetized disk and high/low voltages in circuits.
The value of any position in a binary umber increases by power of 2 with each move from right to left. Hence, in this system, the right most position is units (2⁰) position, the second position from the right is 2’s (2) position, and proceeding in this way, we have 4’s (2) position, 8’s (2ᵌ) position, 16’s (2⁴) position, and so on.
Therefore, decimal equivalent of binary number 1011 (written as 1011₂) is

1011= 1 * 2 ᵌ + 0*2 + 1*2 + 1*2⁰
= 8 + 0 + 2 + 1
= 11

A BIT refers to a Binary Digit in the Binary number system.


THE TABLE GIVEN BELOW SHOWS THE BINARY EQUIVALENT OF SOME DECIMAL NUMBERS.

DECIMAL BINARY
0 0000
1 0001
2 0010
3 0011
4 0100
5 0101
6 0110
7 0111
8 1000
9 1001
10 1010
11 1011
12 1101
13 1101
14 1110

Octal Number System:

The octal number system is a system with less symbols to use, than other conventional number system. Octal is the base 8 number system that uses the digits from 0 to 7, arranged in the series of columns to represent all numerical quantities. Each column and place value has weighted value of 1, 8, 64, and 512 and so on ranging from right to left.
For example:

126₈ = 1* 8 + 1 * 8 + 6 * 8⁰
= (1 * 64) + (2* 8) + (6* 1)
= 64 + 16 + 6
= 86

So, the decimal equivalent of Octal Number 126₈ is 86₁₀
Now, since there are only 8 digits in the Octal number system, 3 bits (2 ᵌ = 8) are sufficient represent an Octal number in a Binary system.

THE TABLE GIVEN BELOW DISPLAYS THAT IN AN OCTAL FORMAT; EACH DIGIT REPRESENTS THREE BINARY DIGITS.


Octal Binary
0 000
1 001
2 010
3 011
4 100
5 101
6 110
7 111

With this table, it is easy to translate between Octal and Binary. For example
42₈ = 100 010₂
65₈= 110 101₂
13₈= 001 001₂


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