Binary to Decimal Conversion Explained
This explanation details how to convert a binary number to its decimal equivalent. Binary is a base-2 system, using only digits 0 and 1, while decimal is a base-10 system.
Understanding Positional Value
In the binary number 110, each digit holds a specific positional value, which is a power of 2. Starting from the rightmost digit:
- The rightmost digit (0) is in the $2^0$ (ones) place.
- The middle digit (1) is in the $2^1$ (twos) place.
- The leftmost digit (1) is in the $2^2$ (fours) place.
Calculating the Decimal Value
To find the decimal equivalent, multiply each binary digit by its corresponding positional value and sum the results.
For the binary number 110:
Decimal Value = ($1 \times 2^2$) + ($1 \times 2^1$) + ($0 \times 2^0$)
| Binary Digit | Positional Value (Power of 2) | Calculation |
|---|---|---|
| 1 | $2^2$ = 4 | $1 \times 4 = 4$ |
| 1 | $2^1$ = 2 | $1 \times 2 = 2$ |
| 0 | $2^0$ = 1 | $0 \times 1 = 0$ |
Summing the results from the calculation:
Decimal Value = $4 + 2 + 0 = 6$
Final Conversion Result
Therefore, the binary number 110 is equivalent to the decimal number 6.
Important Questions from Binary Number System
Match List I with List II
LIST I (Statement) LIST II (Value) A. Base-10 (denary) value of the binary number: 100000 I. 100 B. Internet service provider advertises a download speed of 80 megabits per second. What is the time taken in seconds to download an 80 megabyte file ? II. 14 C. A music file is 80 megabytes in size and MP3 file compression reduces the size of a music file by 90%. The number of MP3 files of the size after compression that can be stored on an 800 MB CD III. 32 D. What is the denary (base-10) equivalent to the hexadecimal digit E? IV. 8 Choose the correct answer from the options given below:
In the context of data stored in a computer, what is a byte?
Which of the following statements is/are correct?
(a) For the sequence of integers represented in binary as 00111, 01001, 01011, P………. the next integer P would be represented as 01101
(b) A byte is a binary number consisting of exactly 8 bits
Choose the correct option:
What is the decimal equivalent of binary number 1100110?
What is the binary equivalent of decimal number 75?
