xplain the wayto Perform Decimal to Binary Conversion.
g.(255)10
II.Convert the following binary numbers toa decimal number.Show all
h.(256)10
steps
f.(224)10
e.(192)10
d.(128)10
c.(127)10
b.(105)10
i.Take your own,at least 4 differentdecimalnumber and convert it to
a.(5)10
binary.
To perform decimal to binary conversion, you can follow these steps:
1. Start with the given decimal number.
2. Divide the number by 2 and note down the quotient and remainder.
3. Continue dividing the quotient by 2 until you reach 0.
4. Write down the remainders in reverse order. These remainders will represent the binary equivalent.
Now, let's convert the decimal numbers:
g. (255)10:
Step 1: Divide 255 by 2, we get quotient 127 and remainder 1.
Step 2: Divide 127 by 2, we get quotient 63 and remainder 1.
Step 3: Divide 63 by 2, we get quotient 31 and remainder 1.
Step 4: Divide 31 by 2, we get quotient 15 and remainder 1.
Step 5: Divide 15 by 2, we get quotient 7 and remainder 1.
Step 6: Divide 7 by 2, we get quotient 3 and remainder 1.
Step 7: Divide 3 by 2, we get quotient 1 and remainder 1.
Step 8: Divide 1 by 2, we get quotient 0 and remainder 1.
Writing down the remainders in reverse order: (255)10 = (11111111)2
h. (256)10:
Step 1: Divide 256 by 2, we get quotient 128 and remainder 0.
Writing down the remainder: (256)10 = (100000000)2
f. (224)10:
Step 1: Divide 224 by 2, we get quotient 112 and remainder 0.
Writing down the remainder: (224)10 = (11100000)2
e. (192)10:
Step 1: Divide 192 by 2, we get quotient 96 and remainder 0.
Writing down the remainder: (192)10 = (11000000)2
d. (128)10:
Step 1: Divide 128 by 2, we get quotient 64 and remainder 0.
Writing down the remainder: (128)10 = (10000000)2
c. (127)10:
Step 1: Divide 127 by 2, we get quotient 63 and remainder 1.
Step 2: Divide 63 by 2, we get quotient 31 and remainder 1.
Step 3: Divide 31 by 2, we get quotient 15 and remainder 1.
Step 4: Divide 15 by 2, we get quotient 7 and remainder 1.
Step 5: Divide 7 by 2, we get quotient 3 and remainder 1.
Step 6: Divide 3 by 2, we get quotient 1 and remainder 1.
Step 7: Divide 1 by 2, we get quotient 0 and remainder 1.
Writing down the remainders in reverse order: (127)10 = (1111111)2
b. (105)10:
Step 1: Divide 105 by 2, we get quotient 52 and remainder 1.
Step 2: Divide 52 by 2, we get quotient 26 and remainder 0.
Step 3: Divide 26 by 2, we get quotient 13 and remainder 0.
Step 4: Divide 13 by 2, we get quotient 6 and remainder 1.
Step 5: Divide 6 by 2, we get quotient 3 and remainder 0.
Step 6: Divide 3 by 2, we get quotient 1 and remainder 1.
Step 7: Divide 1 by 2, we get quotient 0 and remainder 1.
Writing down the remainders in reverse order: (105)10 = (1101001)2
i. Let's take some decimal numbers and convert them to binary:
a. (5)10:
Step 1: Divide 5 by 2, we get quotient 2 and remainder 1.
Step 2: Divide 2 by 2, we get quotient 1 and remainder 0.
Step 3: Divide 1 by 2, we get quotient 0 and remainder 1.
Writing down the remainders in reverse order: (5)10 = (101)2