In binary arithmetic, what is 1111 (binary) plus 0001 (binary) in binary and decimal?

In binary arithmetic, what is 1111 (binary) plus 0001 (binary) in binary and decimal?

• A. 10000 in binary; decimal 16
• B. 1110 in binary; decimal 14
• C. 1000 in binary; decimal 8
• D. 10001 in binary; decimal 17

Answer: (A)

Binary addition works by adding digits from right to left and carrying when the sum reaches 2. When you add 1111 and 0001, the rightmost bits give 1 + 1 = 0 with a carry of 1. Move to the next position: 1 + 0 + carry 1 = 0 with a carry of 1. Do the same for the next two positions, each time producing 0 with a carry of 1. After finishing all four positions, there’s a remaining carry of 1, which becomes a new most-significant bit, yielding 10000. This binary value equals decimal 16 because the 1 sits in the 2^4 place. If you were limited to four bits, you’d have an overflow and couldn’t store 10000 without increasing the width, but the sum itself is correctly 10000 in binary, which is 16 in decimal. The other options would represent different sums (14, 8, or 17) and don’t match the actual addition.

Binary addition works by adding digits from right to left and carrying when the sum reaches 2. When you add 1111 and 0001, the rightmost bits give 1 + 1 = 0 with a carry of 1. Move to the next position: 1 + 0 + carry 1 = 0 with a carry of 1. Do the same for the next two positions, each time producing 0 with a carry of 1. After finishing all four positions, there’s a remaining carry of 1, which becomes a new most-significant bit, yielding 10000. This binary value equals decimal 16 because the 1 sits in the 2^4 place. If you were limited to four bits, you’d have an overflow and couldn’t store 10000 without increasing the width, but the sum itself is correctly 10000 in binary, which is 16 in decimal. The other options would represent different sums (14, 8, or 17) and don’t match the actual addition.