ITPEC IP October 2024 Question 3
As shown in the figure below, decimal numbers 2, 5, 10, and 21 are represented using five (5) squares that are black or white.
A white square indicates 0, and a black square indicates a different positive value that is determined depending on the position of the square. The sum total of the values of the five (5) squares represents a decimal number. Which of the following is the decimal number that is represented by ■■□□□?
Explanation
24 — the squares carry the binary place values 16, 8, 4, 2, 1 from left to right, and ■■□□□ has only the first two black.
Work out each square's value from the examples:
- •2 has only the 4th square black, so the 4th is worth 2
- •10 has the 2nd and 4th black, so the 2nd is worth 10 − 2 = 8
- •5 has the 3rd and 5th black, and 21 has the 1st, 3rd and 5th black, so the 1st is worth 21 − 5 = 16
- •the 3rd and 5th share 5, which fits the doubling pattern as 4 and 1
The values double from right to left, exactly as in a 5-bit binary number, so ■■□□□ is 11000 = 16 + 8 = 24.
Answer (c)
Why not others:
- •(a) 12 — is 8 + 4, the 2nd and 3rd squares: the pattern read one position too far right
- •(b) 20 — is 16 + 4, the 1st and 3rd squares, not the first two
- •(d) 30 — is 16 + 8 + 4 + 2, four black squares instead of two
Key rule: Find unknown place values from the examples by subtraction; when each position is worth double the one to its right, the pattern is simply a binary number.
Basic Theory · AI-written, may contain errors
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