Question

b) IfX=111.101 and Y=101.110. Calculate x + y, and x-y
7
and y-x by 2's complement method.​

Answer 1

Answer:

Difference =-(2 's complement of 110.001) = -1.111

Step-by-step explanation:

Step : 1 Given:

$\begin{aligned}& X=111.101 \\& Y=101.110\end{aligned}$

Now

X+Y  =       111.101

                101.110

               1101.001  

For

$X-Y & =X+2 \text$ 's complement of Y

                 =111.101+010.010

$\begin{aligned}\text { Discard the carry } & =\text { S } 001.111 \text { as number will be positive } \\& =001.111=1.111\end{aligned}$

For

$\begin{aligned}Y-X & =Y+2 \text { 's complement of } X \\& =101.110+000.011=110.001\end{aligned}$

$\because$ There is no carry generated its a negative number.

$\therefore$Difference =-(2 's complement of 110.001) = -1.111

Step : 2 The method of complements is a technique used in mathematics and computing to encrypt a symmetric range of positive and negative integers such that addition may be performed over the whole range using the same algorithm and hardware. Step 1: Express the provided number's absolute value in binary form. To signify that this number is positive, prefix it with 0. Step 2: Complement each bit by flipping the corresponding ones and zeros. Step 3: Increase your outcome by 1.

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