A binary number system with 2n bits, all of the which are 1's has
| A binary number system with 2n bits, all of the which are 1's has the value.
A. 2<sup>2n</sup> - 1
B. 2<sup>2n</sup>
C. 2<sup>2n</sup> + 1
D. 2 × 2<sup>n-1</sup>
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Right Answer is: A
SOLUTION
Concept:
A binary number with n bits has a range from 0 to 2n - 1 in decimal equivalent.
With all the bits = 0, the decimal equivalent is 0.
With all the bits = 1, the decimal equivalent is 2n - 1.
Application:
Given binary number is of 2n bits. The range will be:
When all the bits are 0, the decimal equivalent will be 0.
When all the bits = 1, the decimal equivalent will be 22n - 1.
Example:
Let n = 3 bits. ∴ 2n = 2 × 3 = 6 bits.
With all the bits = 1, we get (111111)2.
The decimal equivalent = 63 = 22n - 1.