Final answer:
The decimal value of 11011001 in an 8-bit unsigned quantity is 217. In two's complement, the decimal value would be -39. The two's complement additive inverse of 11011001 is 00100111. When adding 11011001 and 10010001 in binary, the sum is 101011010. If interpreted as unsigned numbers, the sum does not result in overflow. But if interpreted as signed two's complement numbers, the sum does result in overflow.
Step-by-step explanation:
For an 8-bit unsigned integer, we have a range of numbers from 0 to 255. So, the decimal value of 110110012 would be calculated as follows:
- 1 x 27 + 1 x 26 + 0 x 25 + 1 x 24 + 1 x 23 + 0 x 22 + 0 x 21 + 1 x 20 = 217
For a signed, two's complement quantity, the most significant bit (MSB) is used to represent the sign. If the MSB is 0, then the number is positive. If the MSB is 1, then the number is negative.
In two's complement, to find the additive inverse of a number, we invert all the bits and add 1 to the result. So, the two's complement additive inverse of 110110012 is:
- Invert all the bits: 00100110
- Add 1 to the result: 00100110 + 1 = 00100111
(b) To find the 8-bit binary sum of 110110012 and 100100012, we add the two numbers:
- 11011001
- + 10010001
- ------------------
- 101011010
If we interpret the addends as unsigned numbers, the sum of 110110012 and 100100012 does not result in overflow because the sum does not exceed the maximum value of an 8-bit unsigned integer, which is 255.
If we interpret the addends as signed two's complement numbers, the sum of 110110012 and 100100012 does result in overflow because the sum exceeds the maximum positive value (127) and becomes a negative value.