Final answer:
The maximum and minimum integers representable by a 10-bit 2's complement binary number are +511 and -512 respectively, due to the range determined by the most significant bit being used as a sign bit.
Step-by-step explanation:
The maximum and minimum integers that can be represented by a 10-bit 2's complement binary number system are +511 and -512 respectively. In a 2's complement system, for an n-bit number, the range of representable integers is from -2(n-1) to 2(n-1)-1. Given that we are working with 10 bits, the calculations are as follows:
- Maximum positive integer: 2(10-1) - 1 = 29 - 1 = 512 - 1 = 511
- Minimum negative integer: -2(10-1) = -29 = -512
These limits are due to the fact that the most significant bit in 2's complement binary numbers is used as the sign bit: '0' denotes positive and '1' denotes negative.