Question

If x=(1101) and y=(110), then what is the value of x^2-y^2 in binary number

Answer 1

Answer:

1200101

Step-by-step explanation:

x^2 - y^2

x = 1101 y = 110

x^2 - y^2

= (x+y) (x-y)

= (1101 + 110) (1101 - 110)

= 1211 × 991

= 1200101

Answer 2

Concept

A binary number is a number stated in the binary system or base two numeral system, according to digital technology and mathematics.

Given

we are given $x=(1101)$ and $y=(110)$.

Find

we have to find the value of $x^2-y^2$  in binary number.

Solution

Given $x=(1101)_{2}$ and $y=(110)_{2}$.

Firstly, we will convert the given numbers into decimals.

So, here the rightmost digit is represented by $2^{0}$ then by $2^{1}$ and similarly with others.

The decimal representation of both numbers is

$\begin{aligned}x=\left(1101)_{2}&=1\times 2^{0}+0\times 2^{1}+1\times 2^{2}+1\times 2^{3}\\ &=1+4+8\\ &=13\end{aligned}$

$\begin{aligned}y=\left(110)_{2}&=0\times 2^{0}+1\times 2^{1}+1\times 2^{2}+\\ &=0+2+4\\ &=6\end{aligned}$

Now, we will find $x^2$ and $y^2$, we get

$x^2=169\\y^2=36$

Further, we will find $x^2-y^2$, we get

$\begin{aligned}x^2-y^2&=169-36\\ &=133\end{aligned}$

Now, we will convert this in decimal with base $2$ and write in the form down to up and this will find by diving the number with $2$ again and again, we get the remainder in the form zero or one

$(133)_{10}=(10000101)_{2}$

Hence, the binary number of the given terms square difference $x^2-y^2=(133)_{10}=(10000101)_{2}.$

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