Question
8. From the results of the previous two questions, generalize the range of values (in decimal) that can be represented in any given x number of bits using:
a) Signed magnitude
b) One’s complement
c) Two’s complement
Answer
a)
Signed magnitude: For a given x number of bits, in signed magnitude representation, the range of values that can be represented is as follows:
- Positive values:
- Negative values:
b)
One's complement: For a given x number of bits, in one's complement representation, the range of values that can be represented is as follows:
- Positive values:
- Negative values:
c) Two's complement: For a given x number of bits, in two's complement representation, the range of values that can be represented is as follows:
- Positive values:
- Negative values:
In two's complement representation, one additional negative value can be represented compared to signed magnitude and one's complement. This is due to the elimination of redundancy where both positive and negative zero are represented separately in signed magnitude and one's complement representations.
It's important to note that the range of values assumes the use of all x bits in the representation. If the leftmost (most significant) bit is reserved for the sign, the range of positive values will be slightly reduced to accommodate the sign bit.