Search any question & find its solution
Question:
Answered & Verified by Expert
In the binary equation $(1 \mathrm{pl} 01)_{2}+(10 \mathrm{ql})_{2}=(100 \mathrm{r} 00)_{2}$
where $\mathrm{p}, \mathrm{q}$ and $\mathrm{r}$ are binary digits, what are the possible values of $\mathrm{p}, \mathrm{q}$ and $\mathrm{r}$ respectively?
Options:
where $\mathrm{p}, \mathrm{q}$ and $\mathrm{r}$ are binary digits, what are the possible values of $\mathrm{p}, \mathrm{q}$ and $\mathrm{r}$ respectively?
Solution:
1617 Upvotes
Verified Answer
The correct answer is:
$0,1,0$
$\quad(1 \mathrm{p} 101)_{2}+(10 \mathrm{q} 1)_{2}=(100 \mathrm{r} 00)_{2}$
$\Rightarrow\left(1 \times 2^{4}+\mathrm{p} \times 2^{3}+1 \times 2^{2}+0 \times 2^{1}+1 \times 2^{0}\right)$
$+\left(1 \times 2^{3}+0 \times 2^{2}+q \times 2^{1}+1 \times 2^{0}\right)$
$=1 \times 2^{5}+0+0+\mathrm{r} \times 2^{2}+0+0$
$\Rightarrow 16+8 \mathrm{p}+4+1+8+2 \mathrm{q}+1=32+4 \mathrm{r}$
$\Rightarrow 30+8 p+2 q=32+4 r$
$\Rightarrow 8 \mathrm{p}+2 \mathrm{q}=2+4 \mathrm{r}$
from options, substitute $\mathrm{p}=0, \mathrm{q}=1, \mathrm{r}=0$ we get
$0+2(1)=2+0 \Rightarrow 2=2$.
$\Rightarrow\left(1 \times 2^{4}+\mathrm{p} \times 2^{3}+1 \times 2^{2}+0 \times 2^{1}+1 \times 2^{0}\right)$
$+\left(1 \times 2^{3}+0 \times 2^{2}+q \times 2^{1}+1 \times 2^{0}\right)$
$=1 \times 2^{5}+0+0+\mathrm{r} \times 2^{2}+0+0$
$\Rightarrow 16+8 \mathrm{p}+4+1+8+2 \mathrm{q}+1=32+4 \mathrm{r}$
$\Rightarrow 30+8 p+2 q=32+4 r$
$\Rightarrow 8 \mathrm{p}+2 \mathrm{q}=2+4 \mathrm{r}$
from options, substitute $\mathrm{p}=0, \mathrm{q}=1, \mathrm{r}=0$ we get
$0+2(1)=2+0 \Rightarrow 2=2$.
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.