# Answered! how many unique states of information can be stored in a 16 bit piece of data. overflow is common occurrence in binary arithmetic,…

how many unique states of information can be stored in a 16 bit piece of data.

overflow is common occurrence in binary arithmetic,Using 3 bits of two’s complement,provide an example when overflow would ocuur.

Using 16 bits, we can represent 2^16 = 65536 unique states.

Let us try to understand. For example, using 1 bit , there are 2^1 i.e just 2 states. They are 0 and 1.

using 2 bits , there are 2^2 i.e 4 states ie. 00 , 01, 10 ,11

using 3 bits there are 2^3 i.e 8 states i.e 000, 001,010, 011, 100, 101, 110 , 111

Likewise using n bits we get 2^n different states. Therefore with 16 bits we get 2^16 = 65536 states

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Using 2’s complement, overflow occurs

1. when adding 2 positive number , the result is -ve

2. when adding 2 negative numbers, the result is +ve

Example using 3 bits for signed bits, 1 bits is for sign and remaining 2 bits for numeric part, lets add 2 and 3

2 in 3 bit binary is 010

3 in binary form is 011