Decimal to binary convertion
I 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
I. The conversion from decimal to binary can be done by continuously dividing the decimal number by 2 until the quotient becomes 0. The remainders obtained from each division will be the binary digits in reverse order.
Here are the steps to perform decimal to binary conversion:
1. Start with the decimal number that needs to be converted.
2. Divide the decimal number by 2.
3. Write down the remainder (either 0 or 1).
4. Note the quotient obtained from the division.
5. If the quotient is still greater than 0, repeat steps 2-5 using the quotient as the new decimal number.
6. Continue these steps until the quotient becomes 0.
7. Finally, write down all the remainders in reverse order to get the binary equivalent.
For example, let's convert the decimal number 10 to binary:
1. Start with 10.
2. Divide 10 by 2, the remainder is 0.
3. Note down the remainder (0).
4. The quotient is 5.
5. Repeat the process using 5 as the new decimal number.
6. Divide 5 by 2, the remainder is 1.
7. Note down the remainder (1).
8. The quotient is 2.
9. Repeat the process using 2 as the new decimal number.
10. Divide 2 by 2, the remainder is 0.
11. Note down the remainder (0).
12. The quotient is 1.
13. Repeat the process using 1 as the new decimal number.
14. Divide 1 by 2, the remainder is 1.
15. Note down the remainder (1).
16. The quotient is 0.
17. Since the quotient is 0, we stop the process.
18. The binary equivalent of 10 is 1010.
II. Here are the decimal numbers converted to binary:
a. (5)10 = (101)2
b. (105)10 = (1101001)2
c. (127)10 = (1111111)2
d. (128)10 = (10000000)2
e. (192)10 = (11000000)2
f. (224)10 = (11100000)2
g. (255)10 = (11111111)2
h. (256)10 = (100000000)2
And now, let's take a look at converting some decimal numbers to binary:
i. Let's convert the decimal number 27 to binary:
1. Start with 27.
2. Divide 27 by 2, the remainder is 1.
3. Note down the remainder (1).
4. The quotient is 13.
5. Repeat the process using 13 as the new decimal number.
6. Divide 13 by 2, the remainder is 1.
7. Note down the remainder (1).
8. The quotient is 6.
9. Repeat the process using 6 as the new decimal number.
10. Divide 6 by 2, the remainder is 0.
11. Note down the remainder (0).
12. The quotient is 3.
13. Repeat the process using 3 as the new decimal number.
14. Divide 3 by 2, the remainder is 1.
15. Note down the remainder (1).
16. The quotient is 1.
17. Repeat the process using 1 as the new decimal number.
18. Divide 1 by 2, the remainder is 1.
19. Note down the remainder (1).
20. The quotient is 0.
21. Since the quotient is 0, we stop the process.
22. The binary equivalent of 27 is 11011.