DIGITAL_LOGIC

Question

Which of the following statement is Incorrect for the range of n bits binary
numbers?
a. Range of unsigned numbers is 0 to 2n – 1.
b. Range of signed numbers is –2n – 1 + 1 to 2n – 1 – 1
c. Range of signed 1’s complement numbers is –2n – 1 + 1 to 2n – 1
d. Range of signed 2’s complement numbers is –2n – 1 to 2n – 1 – 1

 

i think b and c both are wrong

Answer 1

Both B and C are Wrong.

Range of Unsigned Representation of Binary Numbers: 0 to 2^n-1

Range of Signed, 1's complement                               : -(2^n-1-1) to (2^n-1 -1)

2's complement Representation of binary number       :  -(2^n-1) to (2^n-1 -1)

For eg: take a binary string of length 3

unsigned (max,min)                  = 111,000 (7,0)

signed (max,min)                      = 011,111(3,-3)

1's complement(max,min)         = 011,100(3,-3)

2's complement(max,min)         = 011, 100(3,-4)

Answer 2

B and C considering that you mean exponential powers. 2^(n-1) not 2n-1

Comments

So the minimum number represented by signed magnitude is -(2^n-1)-1. Now if I put n=4 we get -(2^4-1)-1= -9?

or am I missing something here?

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It's right

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Dude -(2^(n-1)-1) = -7

Range -7 to +7

Answer 3

Correct Answer is D)