Question

question 6
match the letters with the correct answer.
a)
b)
c)
d)
e. 2_{10}+(10110_2 - 1011_2)
a choose
b choose
c choose
d choose
e choose

Explanation:

Step1: Convert binary numbers to decimal

First, convert $10110_2$ and $1011_2$ to decimal.
For $10110_2$, we have $1\times2^4 + 0\times2^3+1\times2^2 + 1\times2^1+0\times2^0=16 + 0+4 + 2+0 = 22_{10}$.
For $1011_2$, we have $1\times2^3+0\times2^2 + 1\times2^1+1\times2^0=8 + 0+2 + 1=11_{10}$.

Step2: Calculate the value of the expression

Calculate $2_{10}+(10110_2 - 1011_2)=2+(22 - 11)=2 + 11=13_{10}$.

Step3: Represent 13 in binary

Divide 13 by 2 successively:
$13\div2 = 6$ remainder $1$;
$6\div2=3$ remainder $0$;
$3\div2 = 1$ remainder $1$;
$1\div2=0$ remainder $1$.
Reading the remainders from bottom - to - top, $13_{10}=1101_2$.
Count the number of yellow (which we can assume represent 1s) and white (represent 0s) bulbs in each option to match with $1101_2$.

Answer:

We need to visually count the bulbs in each option to match with the binary representation of 13 ($1101_2$). Without the visual count of bulbs in each option provided in text form, we can't give a final letter - answer. But the value of the expression $E$ is $13_{10}$ or $1101_2$ in binary.