Final answer:
In a byte using two's complement, the largest positive number is 127, and the largest negative number is -128, determined by setting the sign bit and the value of the remaining bits.
Step-by-step explanation:
The largest positive and negative numbers that can be stored in a byte using two's complement can be found by understanding how two's complement works. A byte consists of 8 bits. In two's complement, the most significant bit (MSB) is used as the sign bit. If the MSB is 0, the number is positive, and if it is 1, the number is negative.
For the largest negative number in a byte, the MSB is 1, and all other bits are 0 following the two's complement rules. This gives us 10000000 in binary, which is -128 in decimal. Note that the range of numbers in two's complement is asymmetric, with one more negative value than positive.