Respuesta :
When you add a zero on the right side of a binary number, its value increases by 2 times that of the previous binary number.
Given: We need to find when we add a 0 to the value of a binary number on the right side.
What are binary numbers?
Binary numbers are those numbers that are represented by 0s and 1s only and it has a base of 2. We can find the value of a binary number in decimal form by multiplying each digit in the binary string with 2 raised to the power of its position(NOTE: We start from the rightmost side where the position value is 0) and then summing up all the values.
For example: Say 1101 is a binary number. To know what the value is we will simply look at the positions then multiply them by 2 raised to the power of their position and then add them all. Let's start from the rightmost side.
At the rightmost side of 1101, we have 1 with position 0, so 2⁰ × 1
Traversing left, the rightmost number (now not including the last) is 0, so
2¹ × 0.
Further, the number at the 2nd position(from the right initially starting from 0) is 1, so 2² × 1
and the number at the third position from the right is 1, so 2³ × 1.
Therefore the number 1101 in decimal form is or we can say that from base 2 form to base 10 forms (decimal numbers having a base of 10) is:
(1101)₂ = 2⁰ × 1 + 2¹ × 0 + 2² × 1 + 2³ × 1
(1101)₂ = 1 + 0 + 4 + 8 = (13)₁₀
Hence 1101 is 13.
Let's solve the given question:
We assume let 1 is a binary number.
The value of 1 in a decimal system or base 10 system is
(1)₂ = 2⁰ × 1
= 1 or (1)₁₀
Adding a 0 on the right-hand side, the binary 1 number becomes 10.
The value of 10 in a decimal system or base 10 system is
(10)₂ = 2⁰ × 0 + 2¹ × 1
= 0 + 1
= 2 or (2)₁₀
Adding 0 on the right-hand side, the binary 10 number becomes 100.
The value of 100 in a decimal system or base 10 system is
(100)₂ = 2⁰ × 0 + 2¹ × 0 + 2² × 1
= 0 + 0 + 4
= 4 or (4)₁₀
From the above three binary numbers 1, 10, and 100 we see that the decimal values are 1, 2, and 4.
Therefore we observe that when we are adding zero on the right-hand side of the binary number, the decimal value is becomes increasing by 2 times the previous number.
Hence, when you add a zero on the right side of a binary number, its value increase by 2 times the previous binary number.
Know more about "binary numbers" here: https://brainly.com/question/8649831
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