Find the binary expansion of 2/3 and determine which machine number x− or x+ (left-shifted, with 23-bit mantissa) is closer to 2/3. Then find the relative rounding error associated with this approximation.

Problem 3: Perform the indicated subtraction with the following unsigned binary numbers by taking the 2's complement of the subtrahend. (a) 11010 - 10001 (b) 11110 - 1110 (c) 101001- 101 Hint: You need to make the no of bits in the two numbers equal by padding Os to the left of the subtrahend before taking its 2's complement.

Question: To find the twos complement of X, take the Boolean complement of each bit of X, and then add 1.  Show that the following is an equivalent definition. For an n-bit integer X, the twos complement of X is formed by treating X as an unsigned integer and calculating (2n - X). My Comments: I'm not exactly sure how to understand what this is asking for. I know that for positive numbers, the left most bit is a 0 to represent a negative value, and for negative numbers, a zero is placed at the left most bit to represent a negative value.

Perform the following additions, assuming 7-bit two's complement binary representation. Show the effect on the status bits (NZVC). Example: Example: Note: that this is a 6-bit example and the questions below are for 7-bit. ex) 101000 + 100000 001000 NZVC 0011 Result was 1001000 but the 1 is carry-out (C-1). Negat ive + Negative should be Negative but positive so overflow (V=1) a) NZVC b) NZVC 1101001 + 1110001 1111111 + 0110101