QuestionConvert the following binary numbers to decimal: 39. $10112$ and 40. $11101_{2}$ .

Studdy Solution

STEP 1

Assumptions1. The numbers are given in binary format (base). . We need to convert these binary numbers into denary (base10) numbers.

STEP 2

We will use the method of binary to decimal conversion. In this method, each digit of the binary number is multiplied by2 raised to the power of its position, starting from0 on the rightmost side. The sum of these products gives the decimal number.
For the first number10112 $10112 =1 \times2^4 +0 \times2^ +1 \times2^2 +1 \times2^1 +2 \times2^0$

STEP 3

Calculate the value of the first number.
$10112 =1 \times16 +0 \times8 +1 \times +1 \times2 +2 \times1$

STEP 4

implify the equation to get the decimal equivalent of the binary number.
$10112 =16 +0 +4 +2 +2 =24$

STEP 5

Now, let's convert the second binary number $11101_{2}$ to decimal using the same method.
$11101_{2} =1 \times2^4 +1 \times2^3 +1 \times2^2 +0 \times2^1 +1 \times2^0$

STEP 6

Calculate the value of the second number.
$11101_{2} =1 \times16 +1 \times8 +1 \times4 +0 \times2 +1 \times1$

STEP 7

implify the equation to get the decimal equivalent of the binary number.
$11101_{2} =16 + +4 +0 +1 =29$ So, the denary (decimal) equivalents of the binary numbers10112 and $11101_{2}$ are24 and29 respectively.

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