There are many techniques that are used to convert numbers from one base to another. In this article, you will learn the conversion of binary to decimal with the help of examples. Here, the following conversion of binary to decimal is explained.
- Binary to Decimal Number System
- Decimal to Binary Number System
- Octal to Binary Number System
- Binary to Octal Number System
- Binary to Hexadecimal Number System
- Hexadecimal to Binary Number System
Binary to Decimal Number System
Steps
◆ Step 1 − Determine the column (positional) value of each digit (this depends on the position of the digit and the base of the number system).
◆ Step 2 − Multiply the obtained column values (in Step 1) by the digits in the corresponding columns.
decimal.
Examples -
Example 1:
(1011) 2 = 1*2⁰ + 1*2¹ + 0*2² + 1*2³
= 1*1 + 1*2 + 0*4 + 1*8
= 1 + 2 + 0 + 8
= 11
Example 2:
(0.011) 2 = 0*2⁰ + 0*2⁻¹ + 1*2⁻² + 1*2⁻³
= 0*1 + 0*1/2 + 1*1/4 + 1*1/8
= 0 + 0 + 0.25 + 0.125
= (0.375)₁₀
Example 3:
(11010.11) 2 = 0*2⁰ + 1*2¹ + 0*2² + 1*2³ + 1*2⁴ + 1*2 ⁻¹ + 1*2 ⁻²
= 0*1 + 1*2 + 0*4 + 1*8 + 1*16 + 1*1/2 + 1*1/4
= 0 + 2 + 0 + 8 + 16 + 0.5 + 0.25
= (26.75)₁₀
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