Question

Convert from octal to binary:
a. 654
b. 7654.123

Answer 1

To convert from octal to binary, divide the given number into its individual digits and convert each digit from octal to binary using the conversion rule.

Step-by-step explanation:

To convert from octal to binary, we can use a simple conversion method. Each digit in the octal number can be represented by 3 bits in the binary number. Let's convert the given numbers:

1. a. 654
   Octal number 654 can be represented as binary 110 101 100.
2. b. 7654.123
   Octal number 7654 can be represented as binary 111 110 101 100.123 cannot be directly converted to binary because it is a fractional part. To convert the fractional part, we can multiply it by 8 and convert the whole part to binary.

For example, 123 * (1/8) = 123 * 0.125 = 0.15625. Converting 0.15625 to binary, we get 0.00100101. Therefore, the final binary representation of 7654.123 is 111 110 101 100.001 001 01.