Binary Number System

Numbers with base value 2 are known as binary numbers. They are represented using two digits i.e. 0 and 1. For example: 01011 represents (0 × 24) + (1 × 23) + (0 × 22) + (1 × 21) + (1 × 20), they represent 0 + 8 + 0 + 2 + 1, and equals to 11. Now we will see how we will represent the digits in binary notation.

 Decimal Number Binary Number 0 0000 1 0001 2 0010 3 0011 4 0100 5 0101 6 0110 7 0111 8 1000 9 1001 10 (A) 1010 11 (B) 1011 12 (C) 1100 13 (D) 1101 14 (E) 1110 15 (F) 1111 16 (10) 10000

Now we will see how to convert a number represented using Binary Number System to decimal number. Suppose we have 100101 which is in binary form. As we discussed above binary number is always written in 0 and 1 form. So we can convert it into decimal form as:

Given number is 100101, we can write given number as:

[(1) x 25] + [(0) + 24] + [(0) x 23] + [(1) x 22] + [(0) x 21] + [(1) x 20] on further solving we get:

= [1 x 32] + [0 x 16] + [0 x 8] + [1 x 4] + [0 x 2] + [1 x 1],

= 32 + 0 + 0 + 4 + 0 + 1 = 37.

This is how we convert binary numbering system to decimal number.
Now we will see the addition procedure of binary number.

 0 + 0 0 0 + 1 1 1 + 0 1 1 + 1 0

Using these conditions we can add binary numbers.

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