I.Explain the wayto Perform Decimal to Binary Conversion.
g.(255)10
h.(256)10
steps
f.(224)10
i.Take your own,at least 4 differentdecimalnumber and convert it to
e.(192)10
II.Convert the following binary numbers toa decimal number.Show all
d.(128)10
c.(127)10
b.(105)10
a.(5)10
binary.
To convert a decimal number to binary, follow these steps:
1. Start with the given decimal number.
2. Divide the decimal number by 2.
3. Write down the remainder (0 or 1).
4. Divide the quotient obtained in step 2 (if any) by 2.
5. Write down the remainder.
6. Repeat steps 4 and 5 until the quotient becomes 0.
7. Write down the remainders in reverse order, and that will be the binary representation of the decimal number.
For example:
g. (255)10
Step 1: Divide 255 by 2. Quotient = 127, Remainder = 1
Step 2: Divide 127 by 2. Quotient = 63, Remainder = 1
Step 3: Divide 63 by 2. Quotient = 31, Remainder = 1
Step 4: Divide 31 by 2. Quotient = 15, Remainder = 1
Step 5: Divide 15 by 2. Quotient = 7, Remainder = 1
Step 6: Divide 7 by 2. Quotient = 3, Remainder = 1
Step 7: Divide 3 by 2. Quotient = 1, Remainder = 1
Step 8: Divide 1 by 2. Quotient = 0, Remainder = 1
Therefore, (255)10 converts to (11111111)2 in binary.
h. (256)10
Step 1: Divide 256 by 2. Quotient = 128, Remainder = 0
Step 2: Divide 128 by 2. Quotient = 64, Remainder = 0
Step 3: Divide 64 by 2. Quotient = 32, Remainder = 0
Step 4: Divide 32 by 2. Quotient = 16, Remainder = 0
Step 5: Divide 16 by 2. Quotient = 8, Remainder = 0
Step 6: Divide 8 by 2. Quotient = 4, Remainder = 0
Step 7: Divide 4 by 2. Quotient = 2, Remainder = 0
Step 8: Divide 2 by 2. Quotient = 1, Remainder = 0
Step 9: Divide 1 by 2. Quotient = 0, Remainder = 1
Therefore, (256)10 converts to (100000000)2 in binary.
To convert binary numbers to decimal, follow these steps:
1. Start with the given binary number.
2. Write down the place values of the binary digits from right to left (2^0, 2^1, 2^2, 2^3, ...).
3. Multiply each binary digit by its corresponding place value.
4. Sum up the products obtained in step 3, and that will be the decimal representation of the binary number.
For example:
d. (128)10
Step 1: Multiply 1 (first binary digit) by 2^7 (place value of the rightmost digit) = 128
Step 2: The sum is 128.
Therefore, (128)10 converts to (10000000)2 in binary.
c. (127)10
Step 1: Multiply 1 (first binary digit) by 2^6 (place value of the rightmost digit) = 64
Step 2: Multiply 1 (second binary digit) by 2^5 = 32
Step 3: Multiply 1 (third binary digit) by 2^4 = 16
Step 4: Multiply 1 (fourth binary digit) by 2^3 = 8
Step 5: Multiply 1 (fifth binary digit) by 2^2 = 4
Step 6: Multiply 1 (sixth binary digit) by 2^1 = 2
Step 7: Multiply 1 (seventh binary digit) by 2^0 = 1
Step 8: The sum is 127.
Therefore, (127)10 converts to (1111111)2 in binary.
b. (105)10
Step 1: Multiply 1 (first binary digit) by 2^6 = 64
Step 2: Multiply 0 (second binary digit) by 2^5 = 0
Step 3: Multiply 1 (third binary digit) by 2^4 = 16
Step 4: Multiply 0 (fourth binary digit) by 2^3 = 0
Step 5: Multiply 1 (fifth binary digit) by 2^2 = 4
Step 6: Multiply 0 (sixth binary digit) by 2^1 = 0
Step 7: Multiply 1 (seventh binary digit) by 2^0 = 1
Step 8: The sum is 105.
Therefore, (105)10 converts to (1101001)2 in binary.
a. (5)10
Step 1: Multiply 1 (first binary digit) by 2^2 = 4
Step 2: Multiply 0 (second binary digit) by 2^1 = 0
Step 3: Multiply 1 (third binary digit) by 2^0 = 1
Step 4: The sum is 5.
Therefore, (5)10 converts to (101)2 in binary.