Sure, I will help you convert each of the given decimal numbers to their binary equivalents. Let's go through each number step by step.
### Conversion Steps:
a) Convert 35 to binary:
1. Divide 35 by 2. The quotient is 17 and the remainder is 1.
2. Divide 17 by 2. The quotient is 8 and the remainder is 1.
3. Divide 8 by 2. The quotient is 4 and the remainder is 0.
4. Divide 4 by 2. The quotient is 2 and the remainder is 0.
5. Divide 2 by 2. The quotient is 1 and the remainder is 0.
6. Divide 1 by 2. The quotient is 0 and the remainder is 1.
Reading the remainders from bottom to top, we get: 100011.
b) Convert 5555 to binary:
1. Divide 5555 by 2. The quotient is 2777 and the remainder is 1.
2. Divide 2777 by 2. The quotient is 1388 and the remainder is 1.
3. Divide 1388 by 2. The quotient is 694 and the remainder is 0.
4. Divide 694 by 2. The quotient is 347 and the remainder is 0.
5. Divide 347 by 2. The quotient is 173 and the remainder is 1.
6. Divide 173 by 2. The quotient is 86 and the remainder is 1.
7. Divide 86 by 2. The quotient is 43 and the remainder is 0.
8. Divide 43 by 2. The quotient is 21 and the remainder is 1.
9. Divide 21 by 2. The quotient is 10 and the remainder is 1.
10. Divide 10 by 2. The quotient is 5 and the remainder is 0.
11. Divide 5 by 2. The quotient is 2 and the remainder is 1.
12. Divide 2 by 2. The quotient is 1 and the remainder is 0.
13. Divide 1 by 2. The quotient is 0 and the remainder is 1.
Reading the remainders from bottom to top, we get: 1010110110011.
c) Convert 22 to binary:
1. Divide 22 by 2. The quotient is 11 and the remainder is 0.
2. Divide 11 by 2. The quotient is 5 and the remainder is 1.
3. Divide 5 by 2. The quotient is 2 and the remainder is 1.
4. Divide 2 by 2. The quotient is 1 and the remainder is 0.
5. Divide 1 by 2. The quotient is 0 and the remainder is 1.
Reading the remainders from bottom to top, we get: 10110.
d) Convert 57 to binary:
1. Divide 57 by 2. The quotient is 28 and the remainder is 1.
2. Divide 28 by 2. The quotient is 14 and the remainder is 0.
3. Divide 14 by 2. The quotient is 7 and the remainder is 0.
4. Divide 7 by 2. The quotient is 3 and the remainder is 1.
5. Divide 3 by 2. The quotient is 1 and the remainder is 1.
6. Divide 1 by 2. The quotient is 0 and the remainder is 1.
Reading the remainders from bottom to top, we get: 111001.
### Summary:
Hence, the binary equivalents of the given decimal numbers are:
- 35 -> 100011
- 5555 -> 1010110110011
- 22 -> 10110
- 57 -> 111001
I hope this detailed explanation helps you understand the process of converting decimal numbers to binary!
