Question

1.Find the 2’s complement of 11111011. What is the decimal value of it

2.Find A-B using 2’s complement if A=1010 and B=11100

3. A) What is the range of numbers in a 4-bit machine if unsigned integer format is used.

B) What is the smallest and largest number when 2’s complement format is used.

Answer 1

Q1)

2's Complement of 11111011 = 00000101

In 2's complement if MSB Bit is 0 Then Number is Positive and If MSB is 1 the Number is negative

Decimal Value of = 00000101 = + 5

Q2)

In 2's complement we represent negative Number by taking 2's complement of its positive value .

A - B = A + 2's Complement of B

A= 01010

B = 2's Complement ( 11100) = 00100

Now add Both

01010

+00100

----------

01110

Result is 01110 = +14

This is how we can do the Subtraction using 2's complement .

Q3)

Part A

in 4 bits we have number ranging from 0000 to 1111

So 0000 = + 0

and 1111 = + 15

Hence we get Range as 0 - 15

Part B)

In 2's Complement form we have range [−2^N−1, 2^N−1 − 1] where N is Number of bits

Here N = 4

- 2^4-1 = -2^3= -8 ,

2^4-1 -1 = 2^3 -1 = 8-1 = 7

Hence Range is -8 To 7

This is how we can solve each problem

Thank You

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