Answer :
Alright, let's convert the given decimal numbers into binary step-by-step.
### Converting Decimal Numbers to Binary
The method to convert a decimal number to binary involves dividing the number by 2 and recording the remainder. You repeat this until the quotient is 0. The binary representation is read from bottom to top (from the last remainder to the first).
#### a) 9
1. 9 ÷ 2 = 4 remainder 1
2. 4 ÷ 2 = 2 remainder 0
3. 2 ÷ 2 = 1 remainder 0
4. 1 ÷ 2 = 0 remainder 1
Reading from bottom to top: 1001
#### f) 55
1. 55 ÷ 2 = 27 remainder 1
2. 27 ÷ 2 = 13 remainder 1
3. 13 ÷ 2 = 6 remainder 1
4. 6 ÷ 2 = 3 remainder 0
5. 3 ÷ 2 = 1 remainder 1
6. 1 ÷ 2 = 0 remainder 1
Reading from bottom to top: 110111
#### b) 10
1. 10 ÷ 2 = 5 remainder 0
2. 5 ÷ 2 = 2 remainder 1
3. 2 ÷ 2 = 1 remainder 0
4. 1 ÷ 2 = 0 remainder 1
Reading from bottom to top: 1010
#### c) 11
1. 11 ÷ 2 = 5 remainder 1
2. 5 ÷ 2 = 2 remainder 1
3. 2 ÷ 2 = 1 remainder 0
4. 1 ÷ 2 = 0 remainder 1
Reading from bottom to top: 1011
#### g) 124
1. 124 ÷ 2 = 62 remainder 0
2. 62 ÷ 2 = 31 remainder 0
3. 31 ÷ 2 = 15 remainder 1
4. 15 ÷ 2 = 7 remainder 1
5. 7 ÷ 2 = 3 remainder 1
6. 3 ÷ 2 = 1 remainder 1
7. 1 ÷ 2 = 0 remainder 1
Reading from bottom to top: 1111100
#### h) 216
1. 216 ÷ 2 = 108 remainder 0
2. 108 ÷ 2 = 54 remainder 0
3. 54 ÷ 2 = 27 remainder 0
4. 27 ÷ 2 = 13 remainder 1
5. 13 ÷ 2 = 6 remainder 1
6. 6 ÷ 2 = 3 remainder 0
7. 3 ÷ 2 = 1 remainder 1
8. 1 ÷ 2 = 0 remainder 1
Reading from bottom to top: 11011000
#### d) 12
1. 12 ÷ 2 = 6 remainder 0
2. 6 ÷ 2 = 3 remainder 0
3. 3 ÷ 2 = 1 remainder 1
4. 1 ÷ 2 = 0 remainder 1
Reading from bottom to top: 1100
#### i) 361
1. 361 ÷ 2 = 180 remainder 1
2. 180 ÷ 2 = 90 remainder 0
3. 90 ÷ 2 = 45 remainder 0
4. 45 ÷ 2 = 22 remainder 1
5. 22 ÷ 2 = 11 remainder 0
6. 11 ÷ 2 = 5 remainder 1
7. 5 ÷ 2 = 2 remainder 1
8. 2 ÷ 2 = 1 remainder 0
9. 1 ÷ 2 = 0 remainder 1
Reading from bottom to top: 101101001
#### e) 18
1. 18 ÷ 2 = 9 remainder 0
2. 9 ÷ 2 = 4 remainder 1
3. 4 ÷ 2 = 2 remainder 0
4. 2 ÷ 2 = 1 remainder 0
5. 1 ÷ 2 = 0 remainder 1
Reading from bottom to top: 10010
#### j) 490
1. 490 ÷ 2 = 245 remainder 0
2. 245 ÷ 2 = 122 remainder 1
3. 122 ÷ 2 = 61 remainder 0
4. 61 ÷ 2 = 30 remainder 1
5. 30 ÷ 2 = 15 remainder 0
6. 15 ÷ 2 = 7 remainder 1
7. 7 ÷ 2 = 3 remainder 1
8. 3 ÷ 2 = 1 remainder 1
9. 1 ÷ 2 = 0 remainder 1
Reading from bottom to top: 111101010
### Converting Binary Numbers to Decimal Numbers
To convert a binary number to a decimal number, multiply each bit by 2 raised to the power of its position, starting from 0 on the right.
##### Example:
1101 (binary) to decimal:
- (1 2^3) + (1 2^2) + (0 2^1) + (1 2^0)
- 8 + 4 + 0 + 1 = 13 (decimal)
Feel free to provide specific binary numbers to be converted to decimal numbers if needed!
### Converting Decimal Numbers to Binary
The method to convert a decimal number to binary involves dividing the number by 2 and recording the remainder. You repeat this until the quotient is 0. The binary representation is read from bottom to top (from the last remainder to the first).
#### a) 9
1. 9 ÷ 2 = 4 remainder 1
2. 4 ÷ 2 = 2 remainder 0
3. 2 ÷ 2 = 1 remainder 0
4. 1 ÷ 2 = 0 remainder 1
Reading from bottom to top: 1001
#### f) 55
1. 55 ÷ 2 = 27 remainder 1
2. 27 ÷ 2 = 13 remainder 1
3. 13 ÷ 2 = 6 remainder 1
4. 6 ÷ 2 = 3 remainder 0
5. 3 ÷ 2 = 1 remainder 1
6. 1 ÷ 2 = 0 remainder 1
Reading from bottom to top: 110111
#### b) 10
1. 10 ÷ 2 = 5 remainder 0
2. 5 ÷ 2 = 2 remainder 1
3. 2 ÷ 2 = 1 remainder 0
4. 1 ÷ 2 = 0 remainder 1
Reading from bottom to top: 1010
#### c) 11
1. 11 ÷ 2 = 5 remainder 1
2. 5 ÷ 2 = 2 remainder 1
3. 2 ÷ 2 = 1 remainder 0
4. 1 ÷ 2 = 0 remainder 1
Reading from bottom to top: 1011
#### g) 124
1. 124 ÷ 2 = 62 remainder 0
2. 62 ÷ 2 = 31 remainder 0
3. 31 ÷ 2 = 15 remainder 1
4. 15 ÷ 2 = 7 remainder 1
5. 7 ÷ 2 = 3 remainder 1
6. 3 ÷ 2 = 1 remainder 1
7. 1 ÷ 2 = 0 remainder 1
Reading from bottom to top: 1111100
#### h) 216
1. 216 ÷ 2 = 108 remainder 0
2. 108 ÷ 2 = 54 remainder 0
3. 54 ÷ 2 = 27 remainder 0
4. 27 ÷ 2 = 13 remainder 1
5. 13 ÷ 2 = 6 remainder 1
6. 6 ÷ 2 = 3 remainder 0
7. 3 ÷ 2 = 1 remainder 1
8. 1 ÷ 2 = 0 remainder 1
Reading from bottom to top: 11011000
#### d) 12
1. 12 ÷ 2 = 6 remainder 0
2. 6 ÷ 2 = 3 remainder 0
3. 3 ÷ 2 = 1 remainder 1
4. 1 ÷ 2 = 0 remainder 1
Reading from bottom to top: 1100
#### i) 361
1. 361 ÷ 2 = 180 remainder 1
2. 180 ÷ 2 = 90 remainder 0
3. 90 ÷ 2 = 45 remainder 0
4. 45 ÷ 2 = 22 remainder 1
5. 22 ÷ 2 = 11 remainder 0
6. 11 ÷ 2 = 5 remainder 1
7. 5 ÷ 2 = 2 remainder 1
8. 2 ÷ 2 = 1 remainder 0
9. 1 ÷ 2 = 0 remainder 1
Reading from bottom to top: 101101001
#### e) 18
1. 18 ÷ 2 = 9 remainder 0
2. 9 ÷ 2 = 4 remainder 1
3. 4 ÷ 2 = 2 remainder 0
4. 2 ÷ 2 = 1 remainder 0
5. 1 ÷ 2 = 0 remainder 1
Reading from bottom to top: 10010
#### j) 490
1. 490 ÷ 2 = 245 remainder 0
2. 245 ÷ 2 = 122 remainder 1
3. 122 ÷ 2 = 61 remainder 0
4. 61 ÷ 2 = 30 remainder 1
5. 30 ÷ 2 = 15 remainder 0
6. 15 ÷ 2 = 7 remainder 1
7. 7 ÷ 2 = 3 remainder 1
8. 3 ÷ 2 = 1 remainder 1
9. 1 ÷ 2 = 0 remainder 1
Reading from bottom to top: 111101010
### Converting Binary Numbers to Decimal Numbers
To convert a binary number to a decimal number, multiply each bit by 2 raised to the power of its position, starting from 0 on the right.
##### Example:
1101 (binary) to decimal:
- (1 2^3) + (1 2^2) + (0 2^1) + (1 2^0)
- 8 + 4 + 0 + 1 = 13 (decimal)
Feel free to provide specific binary numbers to be converted to decimal numbers if needed!
