Question

5. Answer the followings a) Lets computer stored numbers in 8 bits in 2's complement format, what is the largest and smallest number that can be stored? b) In (a) If we add 1 to the largest number what would happen? if we subtract 1 from smallest number what would happen? c) Why exponent is stored as biased exponent in floating point representation? d) In EFLAG register, some bits have given fixed value 0/1.what is rationale behind it?

Answer 1

(a)

Ans:-

an 8-bit unsigned number can represent the values 0 to 255 (11111111). However a two's complement 8-bit number can only represent positive integers from 0 to 127 (01111111), because the rest of the bitcombinations with the most significant bit as '1' represent the negative integers −1 to −128.

Largest Number:- 127 (01111111)

Smallest Number:- -128 (1000 0000)

(b)

Ans:-

In twos complement, when the top bit is 1, the number is - (the inverted number + 1)

So for the example of 1000 0000 (assuming we have 8 bit numbers), that is - (inverted 1000 0000 + 1) = - (0111 1111 + 1) = - (127 + 1) = -128

To create a twos complement of a negative decimal number, you do a similar thing - for a given number invert the bits, and then add 1.

Ie: For -5, the 5 is 0000 0101 (assuming we will be an 8 bit number). Inverted 1111 1010, add 1 = 1111 1011.

For -128, the 128 is 1000 0000 (ignoring the fact at the moment that the top bit would mean -ve for the 8 bit number), Inverted = 0111 1111, add 1 = 1000 0000.

(C)

Ans:-

In IEEE 754 floating point numbers, the exponent is biased in the engineering sense of the word – the value stored is offset from the actual value by the exponent bias. Biasing is done because exponents have to be signed values in order to be able to represent both tiny and huge values, but two's complement, the usual representation for signed values, would make comparison harder.

To solve this problem the exponent is stored as an unsigned value suitable for comparison, and when being interpreted it is converted into an exponent within a signed range by subtracting the bias.

(d)

Ans:-  Prerequisite – Registers of 8085 microproces
The Flag register is a Special Purpose Register. Depending upon the value of result after any arithmetic and logical operation the flag bits become set (1) or reset (0). In 8085 microprocessor, flag register consists of 8 bits and only 5 of them are useful.

The 5 Flag are:-

SİZ AC CY