To convert the binary number (110110.101)2 to octal, hexadecimal, and decimal numbers, follow these steps:

1. Separate the whole number part from the fractional part. In this case, the whole number part is 110110 and the fractional part is 101.

2. Convert the whole number part to octal. Group the binary digits into groups of three, starting from the rightmost digit. If there are not enough digits, add leading zeros. In this case, we have 110 110. Now, convert each group to its octal equivalent: 110 (binary) = 6 (octal). Therefore, the octal representation of the whole number part is 66.

3. Convert the fractional part to octal. Group the binary digits into groups of three, starting from the leftmost digit. If there are not enough digits, add trailing zeros. In this case, we have 101 000. Now, convert each group to its octal equivalent: 101 (binary) = 5 (octal). Therefore, the octal representation of the fractional part is 0.5.

4. Combine the octal representations of the whole number and fractional parts. In this case, the octal representation of (110110.101)2 is 66.5.

5. Convert the binary number to hexadecimal. Group the binary digits into groups of four, starting from the leftmost digit. If there are not enough digits, add leading zeros. In this case, we have 1101 1010 1000. Now, convert each group to its hexadecimal equivalent: 1101 (binary) = D (hex), 1010 (binary) = A (hex), 1000 (binary) = 8 (hex). Therefore, the hexadecimal representation of the binary number is DA8.

6. Convert the binary number to decimal. To convert the whole number part, multiply each digit by 2 raised to the power of its position, starting from the rightmost digit. Add up the results. In this case, we have 1 * 2^5 + 1 * 2^4 + 0 * 2^3 + 1 * 2^2 + 1 * 2^1 + 0 * 2^0 = 32 + 16 + 0 + 4 + 2 + 0 = 54. To convert the fractional part, multiply each digit by 2 raised to the power of its negative position, starting from the leftmost digit. Add up the results. In this case, we have 1 * 2^-1 + 0 * 2^-2 + 1 * 2^-3 = 0.5 + 0 + 0.125 = 0.625. Therefore, the decimal representation of the binary number is 54.625.

In summary, the binary number (110110.101)2 can be expressed as 66.5 (octal), DA8 (hexadecimal), and 54.625 (decimal).

Question

To convert the binary number (110110.101)2 to octal, hexadecimal, and decimal numbers, follow these steps:

1. Separate the whole number part from the fractional part. In this case, the whole number part is 110110 and the fractional part is 101.

2. Convert the whole number part to octal. Group the binary digits into groups of three, starting from the rightmost digit. If there are not enough digits, add leading zeros. In this case, we have 110 110. Now, convert each group to its octal equivalent: 110 (binary) = 6 (octal). Therefore, the octal representation of the whole number part is 66.

3. Convert the fractional part to octal. Group the binary digits into groups of three, starting from the leftmost digit. If there are not enough digits, add trailing zeros. In this case, we have 101 000. Now, convert each group to its octal equivalent: 101 (binary) = 5 (octal). Therefore, the octal representation of the fractional part is 0.5.

4. Combine the octal representations of the whole number and fractional parts. In this case, the octal representation of (110110.101)2 is 66.5.

5. Convert the binary number to hexadecimal. Group the binary digits into groups of four, starting from the leftmost digit. If there are not enough digits, add leading zeros. In this case, we have 1101 1010 1000. Now, convert each group to its hexadecimal equivalent: 1101 (binary) = D (hex), 1010 (binary) = A (hex), 1000 (binary) = 8 (hex). Therefore, the hexadecimal representation of the binary number is DA8.

6. Convert the binary number to decimal. To convert the whole number part, multiply each digit by 2 raised to the power of its position, starting from the rightmost digit. Add up the results. In this case, we have 1 * 2^5 + 1 * 2^4 + 0 * 2^3 + 1 * 2^2 + 1 * 2^1 + 0 * 2^0 = 32 + 16 + 0 + 4 + 2 + 0 = 54. To convert the fractional part, multiply each digit by 2 raised to the power of its negative position, starting from the leftmost digit. Add up the results. In this case, we have 1 * 2^-1 + 0 * 2^-2 + 1 * 2^-3 = 0.5 + 0 + 0.125 = 0.625. Therefore, the decimal representation of the binary number is 54.625.

In summary, the binary number (110110.101)2 can be expressed as 66.5 (octal), DA8 (hexadecimal), and 54.625 (decimal).

Knowee AI · Accepted Answer