(a) Perform the following binary addition. Show your working. 01101011 + 00110101 [3] (b) Explain what is meant by overflow in binary addition. [2] (c) Stat...

(a) Binary addition of 01101011 + 00110101:

Work from right to left, adding corresponding bits plus any carry from the previous column.

  Carry:  0 1 1 1 0 1 1 0
          0 1 1 0 1 0 1 1
        + 0 0 1 1 0 1 0 1
        ------------------
          1 0 1 0 0 0 0 0

Detailed column work (right to left):

1. Column 1 (units): 1 + 1 = 10. Write 0, carry 1.
2. Column 2: 1 + 0 + 1 (carry) = 10. Write 0, carry 1.
3. Column 3: 0 + 1 + 1 (carry) = 10. Write 0, carry 1.
4. Column 4: 1 + 0 + 1 (carry) = 10. Write 0, carry 1.
5. Column 5: 0 + 1 + 0 (carry) = 1. Write 1, carry 0.
6. Column 6: 1 + 1 + 0 = 10. Write 0, carry 1.
7. Column 7: 1 + 0 + 1 (carry) = 10. Write 0, carry 1.
8. Column 8: 0 + 0 + 1 (carry) = 1. Write 1, carry 0.

Result: 10100000. [3]

(b) Overflow occurs when the result of an arithmetic operation exceeds the maximum value that can be stored in the available number of bits. [1] In an 8-bit register, the largest unsigned value is 255 (11111111). If a calculation produces a value above 255, there is a carry out of the most significant bit position, meaning the result cannot fit in 8 bits. [1]

(c) Overflow has not occurred. [1] The result 10100000 fits entirely within 8 bits, and there was no carry generated beyond the 8th bit position during the addition. Both operands were within the 8-bit range, and their sum (107 + 53 = 160) is still within the unsigned 8-bit range of 0 to 255. [1]

(d) 11111111 in denary: 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255. [1]

(e) The maximum value in a 16-bit unsigned register is calculated as \(2^{16} - 1\). [1] This equals 65535. [1] The formula works because 16 bits can represent \(2^{16}\) = 65536 different values (from 0 to 65535), so the largest is 65535.