Chapter 4.2, Problem 39E

Find the decimal expansion of the number the 3n bit binary expansion (101101…101101)₂ (so that the binary expansion is made of n copies of 101).

[Hint: Use the formula for the sum of the terms of geometrical progression.]

One’s complement representations of integers are used to simplify computer arithmetic. To represent positive and negative integers with absolute value less ${\text{2}}^{\pi -\text{1}}$_,a total of n bits used. The leftmost bit is used to represent the sign. A 0 bit in this position is used for positive integers, and a 1 bit this position is used for negative integers. For positive integers, the remaining bits are identical to the binary expansion of the integer, For negative integers, the remaining bits are obtained by first finding the binary expansion of the absolute value of the integer, and then taking the complement of each these bits, where are complement of a 1 is a 0 and the complement of a 0 is a 1.