Decimal 1023 to octal – UGC NET Question

To convert 1023 to octal, we repeatedly divide by 8 and record remainders. Dividing 1023 by 8 gives a quotient of 127 and remainder 7. Dividing 127 by 8 gives 15 with remainder 7, and 15 divided by 8 gives 1 with remainder 7. Reading the remainders from last to first, we get 1777₈, so 1023₁₀ equals 1777₈.

Option A:
Option A, 1770, corresponds to a decimal value slightly less than 1023. If we convert 1770₈ back to decimal, we do not obtain 1023. Therefore, it cannot be the correct octal representation of 1023.

Option B:
Option B, 1775, differs in the last digit from the correct octal representation. This change in the unit place affects the decimal value. Converting 1775₈ gives a number slightly smaller than 1023, so it does not match the given decimal.

Option C:
Option C, 1777, is formed by the sequence of remainders 7, 7, 7 from the division process. Its decimal value is 1×8^3 + 7×8^2 + 7×8 + 7 = 512 + 448 + 56 + 7 = 1023. Thus, it is the correct octal equivalent.

Option D:
Option D, 2000, is equal to 2×8^3 in decimal, which is 2×512 = 1024. This is one more than 1023, so it cannot represent the given decimal value. Therefore, 2000₈ is not the correct octal representation.