The sum 11011$_2$, 11111$_2$ and 10000$_2$ is 10m10n0$_2$. Find the value of m and n.

Analyze the question: We add three binary numbers and compare the result with the pattern 10m10n0₂.

Convert to decimal (the easy way):

• 11011₂ = 16 + 8 + 0 + 2 + 1 = 27
• 11111₂ = 16 + 8 + 4 + 2 + 1 = 31
• 10000₂ = 16

Sum = 27 + 31 + 16 = 74

Convert 74 to binary:

• 74 = 64 + 8 + 2
• 74 = 1001010₂

Check: 64 (2⁶) + 0 (32) + 0 (16) + 8 (2³) + 0 (4) + 2 (2¹) + 0 (1) = 1001010₂

Compare with the pattern 10m10n0₂: The pattern has 7 digits: 1, 0, m, 1, 0, n, 0. Our answer, 1001010, has digits: 1, 0, 0, 1, 0, 1, 0.

So:

• m = 0
• n = 1

Check by direct binary addition:

  11011
  11111
+ 10000
-------

First two: 11011 + 11111 = 111010 (27 + 31 = 58 ✓.) Then 111010 + 010000 = 1001010 (58 + 16 = 74 ✓.)

Answer: C. m = 0, n = 1

Exam tip: For binary addition questions, convert to base 10, add, and convert back. It is usually faster and less error-prone than carrying in binary. Always verify by matching digit positions with the pattern given.