ow to Convert Binary to Decimal Numbers?Describe the stepsof

Question

h.(01001001)2
e.(11100100)2
II.Convert the following binary numbers toa decimal number.Show all steps
d.(01011100)2
c.(11111100)2
f.(00000101)2
i.Take your own,at least 4 differentbinary number and convert it to
a.(0101)2
b.(1001001)2
g.(11111100)2
differentformulas to perform the conversion.
decimal.

Answer 1

To convert a binary number to a decimal number, you can use the following steps:

1. Write down the binary number.
2. Assign powers of 2 to each digit, starting from the rightmost digit. The rightmost digit represents 2^0, the next digit represents 2^1, the next digit represents 2^2, and so on.
3. Multiply each digit of the binary number by its corresponding power of 2.
4. Add up all the results obtained from step 3 to get the decimal equivalent.

Now, let's apply these steps to the given binary numbers:

h. (01001001)2
Step 1: Write down the binary number.
Step 2: Assign powers of 2 to each digit => 2^0, 2^1, 2^2, 2^3, 2^4, 2^5, 2^6, 2^7
Step 3: Multiply each digit by its corresponding power of 2 => 1*2^0 + 0*2^1 + 0*2^2 + 1*2^3 + 0*2^4 + 0*2^5 + 1*2^6 + 0*2^7 = 9
Therefore, the decimal equivalent of (01001001)2 is 9.

e. (11100100)2
Step 1: Write down the binary number.
Step 2: Assign powers of 2 to each digit => 2^0, 2^1, 2^2, 2^3, 2^4, 2^5, 2^6, 2^7
Step 3: Multiply each digit by its corresponding power of 2 => 0*2^0 + 0*2^1 + 1*2^2 + 0*2^3 + 0*2^4 + 1*2^5 + 1*2^6 + 1*2^7 = 228
Therefore, the decimal equivalent of (11100100)2 is 228.

d. (01011100)2
Step 1: Write down the binary number.
Step 2: Assign powers of 2 to each digit => 2^0, 2^1, 2^2, 2^3, 2^4, 2^5, 2^6, 2^7
Step 3: Multiply each digit by its corresponding power of 2 => 0*2^0 + 0*2^1 + 1*2^2 + 1*2^3 + 1*2^4 + 0*2^5 + 1*2^6 + 1*2^7 = 92
Therefore, the decimal equivalent of (01011100)2 is 92.

c. (11111100)2
Step 1: Write down the binary number.
Step 2: Assign powers of 2 to each digit => 2^0, 2^1, 2^2, 2^3, 2^4, 2^5, 2^6, 2^7
Step 3: Multiply each digit by its corresponding power of 2 => 0*2^0 + 0*2^1 + 1*2^2 + 1*2^3 + 1*2^4 + 1*2^5 + 1*2^6 + 1*2^7 = 252
Therefore, the decimal equivalent of (11111100)2 is 252.

f. (00000101)2
Step 1: Write down the binary number.
Step 2: Assign powers of 2 to each digit => 2^0, 2^1, 2^2, 2^3, 2^4, 2^5, 2^6, 2^7
Step 3: Multiply each digit by its corresponding power of 2 => 1*2^0 + 0*2^1 + 1*2^2 + 0*2^3 + 0*2^4 + 0*2^5 + 0*2^6 + 0*2^7 = 5
Therefore, the decimal equivalent of (00000101)2 is 5.

To convert your own binary numbers to decimal, you can follow the same steps:

a. (0101)2
Step 1: Write down the binary number.
Step 2: Assign powers of 2 to each digit => 2^0, 2^1, 2^2, 2^3
Step 3: Multiply each digit by its corresponding power of 2 => 1*2^0 + 0*2^1 + 1*2^2 + 0*2^3 = 5
Therefore, the decimal equivalent of (0101)2 is 5.

b. (1001001)2
Step 1: Write down the binary number.
Step 2: Assign powers of 2 to each digit => 2^0, 2^1, 2^2, 2^3, 2^4, 2^5, 2^6
Step 3: Multiply each digit by its corresponding power of 2 => 1*2^0 + 0*2^1 + 0*2^2 + 1*2^3 + 0*2^4 + 0*2^5 + 1*2^6 = 73
Therefore, the decimal equivalent of (1001001)2 is 73.

g. (11111100)2
Step 1: Write down the binary number.
Step 2: Assign powers of 2 to each digit => 2^0, 2^1, 2^2, 2^3, 2^4, 2^5, 2^6, 2^7
Step 3: Multiply each digit by its corresponding power of 2 => 0*2^0 + 0*2^1 + 1*2^2 + 1*2^3 + 1*2^4 + 1*2^5 + 1*2^6 + 1*2^7 = 252
Therefore, the decimal equivalent of (11111100)2 is 252.

You can convert any binary number to decimal using the same steps provided above.