Question

Given a (very) tiny computer that has a word size of 3 bits, what are the lowest value (negative number) and the highest value (positive number) that this computer can represent in each of the following representations

Answer 1

Answer:

Explanation:

Signed Magnitude

By using two bits, you can represent exactly 2² unique values, which are  namely 00, 01, 10, 11.

In sign-magnitude representation, the largest +ve value is +3 and the largest -ve value is -3. The possible values with this represented are: -3, -2, -1, -0, +0, +1, +2, +3. The corresponding bits are 100, 101, 110, 111, 000, 001, 010, 011 respectively. In this if we will notice there is different value for + 0 and - 0.

Two’s Complement Representation

In this representation, we don’t have a dedicated sign bit like in  Signed Magnitude, but instead it will represent negative values by first inverting all the bits of the positive value and then adding 1. Hence the decimal values are as follows : -4, -3, -2, -1, 0, +1, +2, +3. The 2’s-complement binary representations of these values are: 100, 101, 110, 111, 000, 001, 010, 011 respectively.

Answer 2

Answer:

There are a varied range of possibilities for the computer represent for the given set of inputs. The most common form includes the representation of the sign magnitude for which the representation is in the way:

-3, -2,

-1,

-0,

+0,

+1,

+2,

+3

The representation of two’s complement.

For N bits of data the representation will be − (2N−1−1).