Question at position 14 Two values A = 11111111111111111111111010101 and B = 1111010101 are representations of 2's complement integers.A is largerA and B are equalYou can not tell from the information provided.B is larger

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BlackTom AI · Accepted Answer

Let’s carefully analyze the two’s complement representations and what their bit widths imply about the numeric values.
Option A: "A is larger". The value A = 11111111111111111111111010101 starts with a 1 in the most significant bit, so A is negative in two’s complement. Since A has many more bits (a longer width) than B, A is effectively a negative number with a very large magnitude when interpreted with its given width. In two’s complement, adding more leading 1s to a negative number (i.e., extending the width with sign extension) makes the value more negative. Therefore A is not larger than B; it is typically far less than B. This option mischaracterizes the relationship.
Option B: "A and B are equal". For equality to hold, the bit patterns would need to represent exactly the same integer value within their respective widths. Given that B (1111010101) is a 10-bit pattern and evaluates to -53 in two’s complement, it is highly unlikely that A, a much longer pattern starting with many 1s, represents exactly -53. The extended width for A changes the value unless the lower bits align precisely to reproduce -53 under sign-extended form, which is not the case here. Thus equality is not correct.
Option C: "You can not tell from the information provided." This would be tempting if we lacked the bit widths. However, the representations as given imply specific widths for A and B. A’s width is the length of its bit string, and B’s width is 10 bits. With those widths known, we can compute their values and compare. Therefore, it is possible to determine the relationship, so this option is not correct.
Option D: "B is larger". As noted, B is a 10-bit two’s complement value 1111010101, which equals -53. A, having a long string of leading 1s, represents a negative number with a much larger magnitude (i.e., a more negative value) when interpreted with its own width. In two’s complement, a larger negative magnitude means a smaller numeric value, so B (being -53) is greater than A. Hence this option correctly identifies the larger value between A and B.

Question at position 14 Two values A = 11111111111111111111111010101 and B = 1111010101 are representations of 2's complement integers.A is largerA and B are equalYou can not tell from the information provided.B is larger

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