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Binary number system consists of two digits 0 and 1 and its base is 2. Each digit or bit in binary number system can be 0 or 1. Digital computer represents all kinds of data and information in the binary system.
110011_{2} = 1× 2^{5} + 1× 2^{4} + 0× 2^{3} + 0× 2^{2} + 1× 2^{1} + 1× 2^{0}In order to convert a binary number into a decimal, it is expanded in the power of 2. Then by simplifyingthe expanded form of the binary number, we obtain a decimal number. For example,
1011_{2} = 1× 2^{3} + 0× 2^{2} + 1× 2^{1} + 1× 2^{0}
= 8 + 0 + 2 + 1
∴ 1011_{2} = 11
= 32 + 16 + 0 + 0 + 2 + 1
∴ 110011_{2} = 51
We can convert decimal number into a binary number by using the place value table of the binary system. For example:
Convert 30 into binary system
2^{5} | 2^{4} | 2^{3} | 2^{2} | 2^{1} | 2^{0} |
32 | 16 | 8 | 4 | 2 | 1 |
1 | 1 | 1 | 1 | 0 |
From the table:
or, 30 = 1× 16 + 1× 8 + 1× 4 + 1× 2 + 1× 1
or, 30 = 1× 2^{4} + 1× 2^{3} + 1× 2^{2} + 1× 2^{1} + 1× 2^{0}
∴ 30 = 11110_{2}
Alternative method
We must divide the given number successively by 2 in order to convert decimal number into binary number. The remainder obtained in each successive division is listed in a separate column. For example:
Solution:
1110_{2 }= 1 × 2^{3 }+ 1 × 2^{2} + 1 × 2^{1} + 0 × 2^{0}
= 1 × 8 + 1 × 4 + 1 × 2 + 0
= 8 + 4 + 2
= 14
∴ 1110_{2 }= 14
Solution:
101101_{2 }= 1 × 2^{5} + 0 × 2^{4} + 1 × 2^{3} + 1 × 2^{2} + 0 × 2^{1} + 1 × 2^{2}
= 1 × 32 + 0 + 1 × 8 + 1 × 4 + 0 + 1 × 1
= 32 + 8 + 4 + 1
= 45
∴ 101101_{2 }= 45
Solution:
2^{5} | 2^{4} | 2^{3} | 2^{2} | 2^{1} | 2^{0} |
32 | 16 | 8 | 4 | 2 | 1 |
1 | 1 | 0 | 0 | 1 |
25 = 1 × 16 + 1 × 8 + 0 × 4 + 0 × 2 + 1 × 1
= 1 × 2^{4} + 1 × 2^{3} + 0 × 2^{2} + 0 × 2^{1} + 1 × 2^{0}
= 11001
∴ 25 = 11001_{2}
______ system consists of two digits 0 and 1 and its base is 2.
We must divide the given number successively by ______ in order to convert decimal number into binary number.
In order to convert a binary number into a decimal, it is expanded in the power of ______.
Each digit or bit in binary number system can be _____.
ASK ANY QUESTION ON Binary Number System
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