Explain the way to Perform Decimal to Binary Conversion.
II. Convert the following binary numbers to a decimal number. Show all
steps
a. (5)10
b. (105)10
c. (127)10
d. (128)10
e. (192)10
f. (224)10
g. (255)10
h. (256)10
i. Take your own, at least 4 different decimal number and convert it to
binary�
To perform decimal to binary conversion, you follow these steps:
1. Start with the given decimal number.
2. Divide the decimal number by 2 and write down the remainder.
3. Divide the quotient obtained in step 2 by 2 again and write down the remainder.
4. Repeat step 3 until the quotient becomes 0.
5. Write down the remainders obtained in reverse order to get the binary representation of the decimal number.
Now let's convert the given decimal numbers to binary:
a. (5)10
- Divide 5 by 2: 5 ÷ 2 = 2 remainder 1
- Divide 2 by 2: 2 ÷ 2 = 1 remainder 0
- Divide 1 by 2: 1 ÷ 2 = 0 remainder 1
- Write down the remainders in reverse order: 101
So, (5)10 is equivalent to (101)2 in binary.
b. (105)10
- Divide 105 by 2: 105 ÷ 2 = 52 remainder 1
- Divide 52 by 2: 52 ÷ 2 = 26 remainder 0
- Divide 26 by 2: 26 ÷ 2 = 13 remainder 0
- Divide 13 by 2: 13 ÷ 2 = 6 remainder 1
- Divide 6 by 2: 6 ÷ 2 = 3 remainder 0
- Divide 3 by 2: 3 ÷ 2 = 1 remainder 1
- Divide 1 by 2: 1 ÷ 2 = 0 remainder 1
- Write down the remainders in reverse order: 1101001
So, (105)10 is equivalent to (1101001)2 in binary.
c. (127)10
- Divide 127 by 2: 127 ÷ 2 = 63 remainder 1
- Divide 63 by 2: 63 ÷ 2 = 31 remainder 1
- Divide 31 by 2: 31 ÷ 2 = 15 remainder 1
- Divide 15 by 2: 15 ÷ 2 = 7 remainder 1
- Divide 7 by 2: 7 ÷ 2 = 3 remainder 1
- Divide 3 by 2: 3 ÷ 2 = 1 remainder 1
- Divide 1 by 2: 1 ÷ 2 = 0 remainder 1
- Write down the remainders in reverse order: 1111111
So, (127)10 is equivalent to (1111111)2 in binary.
d. (128)10
- Divide 128 by 2: 128 ÷ 2 = 64 remainder 0
- Divide 64 by 2: 64 ÷ 2 = 32 remainder 0
- Divide 32 by 2: 32 ÷ 2 = 16 remainder 0
- Divide 16 by 2: 16 ÷ 2 = 8 remainder 0
- Divide 8 by 2: 8 ÷ 2 = 4 remainder 0
- Divide 4 by 2: 4 ÷ 2 = 2 remainder 0
- Divide 2 by 2: 2 ÷ 2 = 1 remainder 0
- Divide 1 by 2: 1 ÷ 2 = 0 remainder 1
- Write down the remainders in reverse order: 10000000
So, (128)10 is equivalent to (10000000)2 in binary.
e. (192)10
- Divide 192 by 2: 192 ÷ 2 = 96 remainder 0
- Divide 96 by 2: 96 ÷ 2 = 48 remainder 0
- Divide 48 by 2: 48 ÷ 2 = 24 remainder 0
- Divide 24 by 2: 24 ÷ 2 = 12 remainder 0
- Divide 12 by 2: 12 ÷ 2 = 6 remainder 0
- Divide 6 by 2: 6 ÷ 2 = 3 remainder 0
- Divide 3 by 2: 3 ÷ 2 = 1 remainder 1
- Divide 1 by 2: 1 ÷ 2 = 0 remainder 1
- Write down the remainders in reverse order: 11000000
So, (192)10 is equivalent to (11000000)2 in binary.
f. (224)10
- Divide 224 by 2: 224 ÷ 2 = 112 remainder 0
- Divide 112 by 2: 112 ÷ 2 = 56 remainder 0
- Divide 56 by 2: 56 ÷ 2 = 28 remainder 0
- Divide 28 by 2: 28 ÷ 2 = 14 remainder 0
- Divide 14 by 2: 14 ÷ 2 = 7 remainder 0
- Divide 7 by 2: 7 ÷ 2 = 3 remainder 1
- Divide 3 by 2: 3 ÷ 2 = 1 remainder 1
- Divide 1 by 2: 1 ÷ 2 = 0 remainder 1
- Write down the remainders in reverse order: 11100000
So, (224)10 is equivalent to (11100000)2 in binary.
g. (255)10
- Divide 255 by 2: 255 ÷ 2 = 127 remainder 1
- Divide 127 by 2: 127 ÷ 2 = 63 remainder 1
- Divide 63 by 2: 63 ÷ 2 = 31 remainder 1
- Divide 31 by 2: 31 ÷ 2 = 15 remainder 1
- Divide 15 by 2: 15 ÷ 2 = 7 remainder 1
- Divide 7 by 2: 7 ÷ 2 = 3 remainder 1
- Divide 3 by 2: 3 ÷ 2 = 1 remainder 1
- Divide 1 by 2: 1 ÷ 2 = 0 remainder 1
- Write down the remainders in reverse order: 11111111
So, (255)10 is equivalent to (11111111)2 in binary.
h. (256)10
- Divide 256 by 2: 256 ÷ 2 = 128 remainder 0
- Divide 128 by 2: 128 ÷ 2 = 64 remainder 0
- Divide 64 by 2: 64 ÷ 2 = 32 remainder 0
- Divide 32 by 2: 32 ÷ 2 = 16 remainder 0
- Divide 16 by 2: 16 ÷ 2 = 8 remainder 0
- Divide 8 by 2: 8 ÷ 2 = 4 remainder 0
- Divide 4 by 2: 4 ÷ 2 = 2 remainder 0
- Divide 2 by 2: 2 ÷ 2 = 1 remainder 0
- Divide 1 by 2: 1 ÷ 2 = 0 remainder 1
- Write down the remainders in reverse order: 100000000
So, (256)10 is equivalent to (100000000)2 in binary.
To convert your own decimal numbers to binary, follow the same steps explained above. Divide the decimal number by 2 repeatedly, noting down the remainders, until the quotient becomes 0, and then reverse the order of the remainders to obtain the binary representation.