Convert binary to decimal 10110110
The Correct Answer and Explanation is:
To convert the binary number 10110110 into decimal, we need to understand how binary (base 2) numbers work. Each digit in a binary number represents a power of 2, starting from the rightmost digit (the least significant bit) and moving left, with the exponent increasing by 1 each time.
Step-by-Step Conversion:
- Write the binary number with corresponding powers of 2:
The binary number 10110110 has 8 digits, so we assign powers of 2 starting from (2^0) on the right: [
1 \times 2^7, 0 \times 2^6, 1 \times 2^5, 1 \times 2^4, 0 \times 2^3, 1 \times 2^2, 1 \times 2^1, 0 \times 2^0
] - Calculate the value of each position:
- (1 \times 2^7 = 128)
- (0 \times 2^6 = 0)
- (1 \times 2^5 = 32)
- (1 \times 2^4 = 16)
- (0 \times 2^3 = 0)
- (1 \times 2^2 = 4)
- (1 \times 2^1 = 2)
- (0 \times 2^0 = 0)
- Add the results:
Now, we add up all the values from the above steps:
[
128 + 0 + 32 + 16 + 0 + 4 + 2 + 0 = 182
]
Thus, the decimal equivalent of the binary number 10110110 is 182.
Explanation:
Binary is a base-2 numeral system, meaning it uses only two digits: 0 and 1. Each digit is called a bit. The place value of each bit is a power of 2, similar to how place values in the decimal system are powers of 10. Starting from the rightmost bit (the least significant bit), the values increase in powers of 2: (2^0, 2^1, 2^2, \dots).
In the case of 10110110, each digit is multiplied by the corresponding power of 2 and then summed up. The ones in the binary number represent the powers of 2 that should be included in the total, while the zeros indicate that those particular powers of 2 are not included in the sum.
The result, 182, is the decimal equivalent of the binary number 10110110.