Yes, it it possible for two 4-bit numbers and a carry-in to result in a number too big to represent using 4 sum bits and a carry-out bit.
What is the binary adder about?
The Binary Adder is a popular and highly practical combinational logic circuit that can be built with just a few simple logic gates and has the ability to add up to four binary integers.
Two single bit binary values, A and B, can be "added" together using a simple binary adder circuit that can be created using common AND and Ex-OR gates. The maximum feasible number with 4 bits is binary 1111 or decimal 15. Although 4 bits in BCD can represent values up to 15, anything greater than 9 is illegitimate.
As a result, it is difficult to perform genuine decimal arithmetic, such as addition, as adding 1001 (9) to 0111 (7) results in an incorrect number. Managing that becomes challenging, etc.
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