If (11101011) 2is converted to decimal system, then the resulting number is
235
To convert a binary number to a decimal number, we use the concept of place values. In the binary system (base 2), each digit's place value is a power of 2. Starting from the rightmost digit (the least significant bit), the place values are \(2^0, 2^1, 2^2\), and so on, increasing by one for each position to the left.
The given binary number is (11101011)₂.
Let's list the digits and their corresponding place values (powers of 2):
| Binary Digit | Position (from right, starting at 0) | Place Value (Power of 2) |
|---|---|---|
| 1 | 7 | \(2^7\) |
| 1 | 6 | \(2^6\) |
| 1 | 5 | \(2^5\) |
| 0 | 4 | \(2^4\) |
| 1 | 3 | \(2^3\) |
| 0 | 2 | \(2^2\) |
| 1 | 1 | \(2^1\) |
| 1 | 0 | \(2^0\) |
To find the decimal equivalent, we multiply each binary digit by its corresponding place value (power of 2) and then sum up all the results. Remember, any power of 2 multiplied by 0 will be 0.
Let's calculate the powers of 2:
- \(2^0 = 1\)
- \(2^1 = 2\)
- \(2^2 = 4\)
- \(2^3 = 8\)
- \(2^4 = 16\)
- \(2^5 = 32\)
- \(2^6 = 64\)
- \(2^7 = 128\)
Now, let's perform the multiplication and summation for the binary number (11101011)₂:
\((11101011)_2 = (1 \times 2^7) + (1 \times 2^6) + (1 \times 2^5) + (0 \times 2^4) + (1 \times 2^3) + (0 \times 2^2) + (1 \times 2^1) + (1 \times 2^0)\) \(= (1 \times 128) + (1 \times 64) + (1 \times 32) + (0 \times 16) + (1 \times 8) + (0 \times 4) + (1 \times 2) + (1 \times 1)\) \(= 128 + 64 + 32 + 0 + 8 + 0 + 2 + 1\) \(= 235\)
So, the binary number (11101011)₂ is equal to 235 in the decimal system.
Revision Table: Binary to Decimal Conversion
| Binary Number | Decimal Conversion Process | Decimal Result |
|---|---|---|
| (11101011)₂ | \(1 \times 2^7 + 1 \times 2^6 + 1 \times 2^5 + 0 \times 2^4 + 1 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 1 \times 2^0\) | 235 |
Additional Information: Number Systems
Understanding different number systems like binary and decimal is fundamental in computing and mathematics. Here's a brief overview:
- Binary System (Base 2): Uses only two digits, 0 and 1. It's the native language of computers because it can be easily represented by electrical states (on/off, high/low voltage).
- Decimal System (Base 10): Uses ten digits, 0 through 9. This is the number system we use in our everyday lives.
- Place Value: In any number system, the position of a digit determines its value. This value is the digit multiplied by the base raised to the power of its position (starting from 0 on the right).
- Other Systems: Other common number systems include Octal (base 8, digits 0-7) and Hexadecimal (base 16, digits 0-9 and A-F). These are often used in computing as a shorthand for binary numbers. Converting between these bases and decimal follows similar principles of place value.
Similar Questions
What is (1110011) 2÷ (10111) 2equal to ?
If x 3 + y 3= (100010111) 2and x + y = (11111) 2, then what is (x - y) 2 + xy equal to ?
The number (1101101 + 1011011) 2can be written in decimal system as
A binary number is represented by (cdccddcccddd) 2, where c > d. What is its decimal equivalent?
The sum of the binary numbers (11011) 2, (10110110)2 and (10011x0y) 2is the binary number (101101101) 2. What are the values of x and y?
The remainder and quotient of the binary division (101110) 2by (110) 2are respectively
In the binary equation (1p101) 2+ (10q1) 2= (100r00) 2
Where p, q and r are binary digits, what are the possible values of p, q and r respectively?If the number 235 in decimal system is converted into binary system, then what is the resulting number?
What is the binary equivalent of the decimal number 0.3125?
What is (1000000001) 2– (0.0101) 2equal to?
Important Questions from Binary Operations
Multiplication of 111 2by 101 2is
Let * be binary operation defined on R by \(\rm p * q=\frac{p+q}{2}, \forall \) p, q ∈ R. The operation is:
Convert 29 into binary.
A. 10101
B. 11110
C. 11101
D. 11001
The product of the two binary numbers 011 and 110 is:
If G is the set of integer numbers, and a.b = a – b, ∀ a, b ∈ G, then G is
