(a) Perform the following binary additions. Show your working including any carries. [6] Addition Working Result 0110 + 0011 10110 + 01101 11111 + 00001 (b)...

(a) Binary additions with carries shown. [6]

Addition 1: 0110 + 0011

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

Working right to left: 0+1=1, 1+1=10 (write 0 carry 1), 1+0+carry 1=10 (write 0 carry 1), 0+0+carry 1=1. Result: 1001. [2]

Addition 2: 10110 + 01101

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

Result: 100011. [2]

Addition 3: 11111 + 00001

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

The carry propagates all the way through. Result: 100000. [2]

(b) Verification of the first addition in denary: [2]

• 0110 = 6
• 0011 = 3
• 1001 = 9
• 6 + 3 = 9, confirming the binary result is correct.

(c) Overflow occurs when the result of a binary addition requires more bits than the system can store. [2] With 8-bit numbers, the maximum unsigned value is 255 (11111111). If two 8-bit numbers add to more than 255, the result needs a 9th bit that cannot be stored, producing an incorrect value. For example, 11111111 + 00000001 = 100000000, but only the lower 8 bits (00000000 = 0) would be kept.

(d) Overflow in binary addition happens when the sum exceeds the bit capacity. [1] For instance, adding 11111111 (255) and 00000001 (1) in an 8-bit register produces 100000000, which requires 9 bits. Since only 8 bits are available, the result wraps to 00000000 (0), which is incorrect.