20.5k views
0 votes
Complete the binary addition with the numbers in 8-bit 2’s complement. verifyyour answer in decimal. show all your work. which problems have an overflow?

A. 00101110 + 00111111
B. 01101001 + 10010000
C. 10110001 + 11000001
D. 11001000 + 11010110

User Poashoas
by
8.2k points

1 Answer

3 votes

Final answer:

To perform binary addition with numbers in 8-bit 2's complement, align the numbers vertically, add them column by column, and convert the binary sum to decimal.

Step-by-step explanation:

To perform binary addition with numbers in 8-bit 2's complement, follow these steps:

  1. Align the numbers vertically.
  2. Add the numbers column by column, starting from the rightmost column.
  3. If there is a carry from the previous column, add it to the sum.
  4. If the sum is greater than 1, write down the rightmost bit of the sum and carry the leftmost bit to the next column.
  5. Repeat this process until all columns are added.

To verify the answer in decimal, convert the binary sum to decimal.

For example:

A. 00101110 + 00111111 = 01101101 (binary sum)

To convert 01101101 to decimal, it is 109.

None of the problems have an overflow.

The binary addition question relates to 8-bit 2's complement arithmetic. Problems C and D have an overflow because the result requires an extra bit to represent. Binary operations and overflow detection are important mathematics concepts.

The subject of the question is binary addition using 8-bit 2's complement representation. Overflow occurs in binary addition when the result is outside the range that can be represented with the given number of bits.

User UfguFugullu
by
8.8k points