Question

please answer this question in return you get 15 points
write the equivalent of the following binary numbers
1. (10101)2
2. (1011)2
3. (1110)2​

Answer 1

Answer:

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Explanation:

1) Step 1: Write down the binary number:

10101

Step 2: Multiply each digit of the binary number by the corresponding power of two:

1x24 + 0x23 + 1x22 + 0x21 + 1x20

Step 3: Solve the powers:

1x16 + 0x8 + 1x4 + 0x2 + 1x1 = 16 + 0 + 4 + 0 + 1

Step 4: Add up the numbers written above:

16 + 0 + 4 + 0 + 1 = 21.

So, 21 is the decimal equivalent of the binary number 10101.

2)Step 1: Write down the binary number:

1011

Step 2: Multiply each digit of the binary number by the corresponding power of two:

1x23 + 0x22 + 1x21 + 1x20

Step 3: Solve the powers:

1x8 + 0x4 + 1x2 + 1x1 = 8 + 0 + 2 + 1

Step 4: Add up the numbers written above:

8 + 0 + 2 + 1 = 11.

So, 11 is the decimal equivalent of the binary number 1011.

3)Step 1: Write down the binary number:

1110

Step 2: Multiply each digit of the binary number by the corresponding power of two:

1x23 + 1x22 + 1x21 + 0x20

Step 3: Solve the powers:

1x8 + 1x4 + 1x2 + 0x1 = 8 + 4 + 2 + 0

Step 4: Add up the numbers written above:

8 + 4 + 2 + 0 = 14.

So, 14 is the decimal equivalent of the binary number 1110.