100112 + *****2 + 111002 + 1012 = 10011112

Analyze the question: The numbers are in base 2 (binary). The question reads 10011₂ + ?????₂ + 11100₂ + 101₂ = 1001111₂, and we need the missing binary number.

Concept: Convert to base 10, solve for the unknown, then convert back to binary (or work directly in binary).

Step 1: Convert the known numbers to base 10

• 10011₂ = 16 + 0 + 0 + 2 + 1 = 19
• 11100₂ = 16 + 8 + 4 = 28
• 101₂ = 4 + 0 + 1 = 5
• 1001111₂ = 64 + 0 + 0 + 8 + 4 + 2 + 1 = 79

Step 2: Find the missing number

19 + x + 28 + 5 = 79 52 + x = 79 x = 27

Step 3: Convert 27 to binary

27 = 16 + 8 + 0 + 2 + 1 = 11011₂

Step 4: Check the options

• A. 1111₂ = 15
• B. 11011₂ = 27 ✔
• C. 10111₂ = 23
• D. 11001₂ = 25

Verification: 19 + 27 + 28 + 5 = 79 ✔

Answer: B (11011₂)

Tip: In binary-addition questions with a missing number, convert everything to base 10, do the arithmetic, then convert back. Powers of 2 to memorise: 1, 2, 4, 8, 16, 32, 64, 128.