Question

module 1: hardware and software quiz 1 a* started: sep 5 at 2:27pm quiz instructions module 1: hardware and software quiz 1 question 5 15 pts 100₂(1011₂ + 10₁₀) = 1010100 base 2 1010001 base 2 1101100 base 2 48 base 10 < previous

Explanation:

Step1: Convert binary to decimal

$1011_2=1\times2^3 + 0\times2^2+1\times2^1 + 1\times2^0=8 + 0+2 + 1 = 11_{10}$
$100_2=1\times2^2+0\times2^1 + 0\times2^0=4_{10}$

Step2: Add numbers in decimal

$1011_2+10_{10}=11 + 10=21_{10}$

Step3: Multiply in decimal

$100_2\times(1011_2 + 10_{10})=4\times21 = 84_{10}$

Step4: Convert result to binary

Divide 84 by 2 successively:
$84\div2 = 42\cdots\cdots0$
$42\div2=21\cdots\cdots0$
$21\div2 = 10\cdots\cdots1$
$10\div2=5\cdots\cdots0$
$5\div2 = 2\cdots\cdots1$
$2\div2=1\cdots\cdots0$
$1\div2 = 0\cdots\cdots1$
Reading the remainders from bottom - to - top, $84_{10}=1010100_2$

Answer:

1010100 base 2