Final answer:
To convert 5613.90625 to binary via octal, the integer part 5613 becomes 12715 in octal and then converts to 001010111001101 in binary. The fractional part .90625 becomes .700000 in octal and then converts to .111 in binary. Combining both gives a binary number of 001010111001101.111.
Step-by-step explanation:
To convert the decimal number 5613.90625 to binary via octal, we first need to convert the integer part and the fractional part separately into octal and then convert each octal digit into its binary equivalent.
Starting with the integer part, 561310 in octal is 127158. Each octal digit can be converted to a 3-bit binary number. So, 127158 converts to binary as follows:
- 18 = 0012
- 28 = 0102
- 78 = 1112
- 18 = 0012
- 58 = 1012
Combining these gives us the binary number for the integer part: 0010101110011012.
For the fractional part .9062510, the octal equivalent is .7000008. Converting these octal digits to binary gives us:
Since there are no other non-zero digits in the octal fractional part, we don't need to proceed with further conversion. So, the binary equivalent for the fractional part is .111
Combining both parts, the binary number of 5613.9062510 through octal is 001010111001101.1112.