A magnitude comparator determines whether one binary value is smaller, equal or larger than another. For unsigned numbers, start at the most significant bit: the first differing bit decides the order. Equality requires every corresponding bit to match.
Worked example
Compare unsigned A = 1010 and B = 1001. The first two bits match. At the third bit from the left, A has 1 and B has 0, so A > B. You can also confirm their decimal values, 10 and 9.
What to watch for
A simple unsigned comparison is not a signed comparison. In twos complement, a leading one denotes a negative value and must be interpreted accordingly.
Try it yourself
Are unsigned 0111 and 1000 ordered the same way when read as four-bit twos complement?
Answer: No. Unsigned, 7 < 8. Signed, they represent +7 and −8, so the first is larger.
How to study this topic
Name each input and define its active level before drawing gates. Follow one data path at a time, then check the other combinations. A complete specification is the best starting point for a reliable circuit.
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Digital Electronics