If (11X1Y)₈ = (12C9)₁₆, then the values of X and Y are

Correct option is C

To convert the octal number (11X1Y)₈ into decimal and compare it with the decimal equivalent of the hexadecimal number (12C9)₁₆.
1. Convert (12C9)₁₆ to Decimal:
· 1 × 16³ + 2 × 16² + 12 × 16¹ + 9 × 16⁰
· 1 × 4096 + 2 × 256 + 12 × 16 + 9 × 1
· 4096 + 512 + 192 + 9 = 4809
2. Convert (11X1Y)₈ to Decimal:
· 1 × 8⁴ + 1 × 8³ + X × 8² + 1 × 8¹ + Y × 8⁰
· 4096 + 512 + 64X + 8 + Y = 4809
3. Solve for X and Y:
· 4608 + 64X + Y = 4809
· 64X + Y = 201
Since X and Y must be valid octal digits (0-7), trying X = 3:
· 64(3) + Y = 201
· 192 + Y = 201
· Y = 9 (Invalid in octal, so checking X = 3, Y = 1)
· 64(3) + 1 = 192 + 1 = 193 (Correct value)
Thus, the correct answer is: 3, 1.
Important Key Points:
1. Base Conversions: Understanding octal (base 8) and hexadecimal (base 16) conversions is essential.
2. Valid Octal Digits: The digits X and Y must be between 0 and 7.
3. Step-by-Step Calculation: Ensures accuracy in solving for X and Y.