Question

For each of the following signed numbers: what are the minimum and maximum values it can represent?

3 bit minimum & Maximum

5 bit minimum & Maximum

Answer 1

a) Singed representation of number as the name suggest is a method to represent both positive and negative numbers.

So for 3 bits in general we can have 2³ patters. This is because we have 3 bits and each bit will have 3 choices. So total no. of choices = 2 * 2 * 2, which is nothing but 2³.

But we have represent both positve and negative no.. So we divide the total no.'s into two equal parts, each having 2² = 4 terms.

Here the MSB (Most Significant Bit - the left most bit) is used to represent the sign of the number. If the MSB is 0 then the no. is positive and if the MSB is 1 then the no. is negative. For the rest of no. we directly evaluate the decimal equivalent of the no..

000 = 0
001 = 1
010 = 2
011 = 3
------------
100 = -0
101 = -1
110 = -2
111 = -3

So it range of no.'s we can represent using the signed notation is is (-3, 3).

b) If we try to generalize we can clearly see that the no. we can represnt using n-bits in signed representation is (-(2^n-1-1) to 2^n-1-1).

So with 5 bits we can represent no. from (-15 to 15).

Hope this helps. If you have any queries or suggestions regarding the answers please leave them in the comments section so I can update and improve the answer. Thank you