Convert the binary expression 11101010.1101 into:
Decimal equivalent
BCD Format
Decimal equivalent: 234.8125
BCD Format: 0010 0011 0100 . 1000
To convert the binary expression 11101010.1101 into decimal equivalent, you can follow these steps:
1. Split the binary expression into two parts: the integer part and the fractional part.
Integer part: 11101010
Fractional part: 1101
2. Convert the integer part to decimal.
The integer part is 11101010. To convert this binary number to decimal, we can use the positional notation. Each digit in the binary number represents a power of 2, starting from right to left. Therefore, the decimal equivalent of the integer part would be:
(1 * 2^7) + (1 * 2^6) + (1 * 2^5) + (0 * 2^4) + (1 * 2^3) + (0 * 2^2) + (1 * 2^1) + (0 * 2^0) = 234
3. Convert the fractional part to decimal.
The fractional part is 1101. To convert this binary number to decimal, we can use the positional notation. Each digit in the binary number represents a negative power of 2, starting from left to right. Therefore, the decimal equivalent of the fractional part would be:
(1 * 2^-1) + (1 * 2^-2) + (0 * 2^-3) + (1 * 2^-4) = 0.8125
4. Combine the decimal equivalent of the integer and fractional parts.
Decimal equivalent = 234 + 0.8125 = 234.8125
To convert the binary expression 11101010.1101 into BCD (Binary Coded Decimal) format, you can follow these steps:
1. Convert the integer part to BCD format.
The integer part is 11101010. To convert this binary number to BCD format, group the binary digits into groups of 4, starting from the rightmost digit. If there are not enough digits to form a group of 4, add leading zeros.
11101010 -> 1110 1010
Convert each group of 4 binary digits to decimal, resulting in:
1110 -> 14
1010 -> 10
The BCD format of the integer part is: 1410
2. Convert the fractional part to BCD format.
The fractional part is 1101. To convert this binary number to BCD format, group the binary digits into groups of 4, starting from the leftmost digit. If there are not enough digits to form a group of 4, add trailing zeros.
1101 -> 1101 0000
Convert each group of 4 binary digits to decimal, resulting in:
1101 -> 13
0000 -> 0
The BCD format of the fractional part is: 1300
3. Combine the BCD formats of the integer and fractional parts.
BCD Format = 1410.1300