Answer :
Certainly! Let's go through the process of converting each of these base ten numbers to base two (binary) step by step.
For each number:
1. 63
To convert 63 to binary:
- Divide 63 by 2, the quotient is 31, remainder is 1.
- Divide 31 by 2, the quotient is 15, remainder is 1.
- Divide 15 by 2, the quotient is 7, remainder is 1.
- Divide 7 by 2, the quotient is 3, remainder is 1.
- Divide 3 by 2, the quotient is 1, remainder is 1.
- Divide 1 by 2, the quotient is 0, remainder is 1.
- Reading the remainders from bottom to top, 63 in binary is 111111.
2. 64
To convert 64:
- Divide 64 by 2, the quotient is 32, remainder is 0.
- Divide 32 by 2, the quotient is 16, remainder is 0.
- Divide 16 by 2, the quotient is 8, remainder is 0.
- Divide 8 by 2, the quotient is 4, remainder is 0.
- Divide 4 by 2, the quotient is 2, remainder is 0.
- Divide 2 by 2, the quotient is 1, remainder is 0.
- Divide 1 by 2, the quotient is 0, remainder is 1.
- 64 in binary is 1000000.
3. 65
Convert 65:
- 65 divided by 2 gives remainder 1 (quotient 32).
- Repeat the steps as for 64 with one more leading 1.
- Binary is 1000001.
4. 49
For 49:
- Keep dividing and noting remainders: 1 -> 0 -> 0 -> 1 -> 1 -> 0.
- Binary is 110001.
5. 100
For 100:
- Divide and take remainders: 0 -> 0 -> 1 -> 0 -> 0 -> 1.
- Binary is 1100100.
6. 129
Convert 129:
- Divide and note: 1 -> 0 -> 0 -> 0 -> 0 -> 0 -> 1.
- Binary is 10000001.
7. 54
For 54:
- Divide for remainders: 0 -> 1 -> 1 -> 0 -> 1.
- Binary is 110110.
8. 72
Convert 72:
- Remainders: 0 -> 0 -> 1 -> 0 -> 0 -> 1.
- Binary is 1001000.
9. 101
For 101:
- Division gives remainders: 1 -> 0 -> 1 -> 0 -> 1.
- Binary is 1100101.
10. 120
Convert 120:
- Divide for bits: 0 -> 0 -> 1 -> 1 -> 1.
- Binary is 1111000.
11. 89
Convert 89:
- Calculate remainders: 1 -> 0 -> 1 -> 1 -> 0 -> 1.
- Binary is 1011001.
12. 194
Convert 194:
- Divide, noting remainders: 0 -> 1 -> 0 -> 0 -> 0 -> 1 -> 1.
- Binary is 11000010.
Each quotient division step helps us write the binary equivalent by reading from bottom up, compiling each remainder into the final binary number. These are your base ten numbers converted into base two (binary).
For each number:
1. 63
To convert 63 to binary:
- Divide 63 by 2, the quotient is 31, remainder is 1.
- Divide 31 by 2, the quotient is 15, remainder is 1.
- Divide 15 by 2, the quotient is 7, remainder is 1.
- Divide 7 by 2, the quotient is 3, remainder is 1.
- Divide 3 by 2, the quotient is 1, remainder is 1.
- Divide 1 by 2, the quotient is 0, remainder is 1.
- Reading the remainders from bottom to top, 63 in binary is 111111.
2. 64
To convert 64:
- Divide 64 by 2, the quotient is 32, remainder is 0.
- Divide 32 by 2, the quotient is 16, remainder is 0.
- Divide 16 by 2, the quotient is 8, remainder is 0.
- Divide 8 by 2, the quotient is 4, remainder is 0.
- Divide 4 by 2, the quotient is 2, remainder is 0.
- Divide 2 by 2, the quotient is 1, remainder is 0.
- Divide 1 by 2, the quotient is 0, remainder is 1.
- 64 in binary is 1000000.
3. 65
Convert 65:
- 65 divided by 2 gives remainder 1 (quotient 32).
- Repeat the steps as for 64 with one more leading 1.
- Binary is 1000001.
4. 49
For 49:
- Keep dividing and noting remainders: 1 -> 0 -> 0 -> 1 -> 1 -> 0.
- Binary is 110001.
5. 100
For 100:
- Divide and take remainders: 0 -> 0 -> 1 -> 0 -> 0 -> 1.
- Binary is 1100100.
6. 129
Convert 129:
- Divide and note: 1 -> 0 -> 0 -> 0 -> 0 -> 0 -> 1.
- Binary is 10000001.
7. 54
For 54:
- Divide for remainders: 0 -> 1 -> 1 -> 0 -> 1.
- Binary is 110110.
8. 72
Convert 72:
- Remainders: 0 -> 0 -> 1 -> 0 -> 0 -> 1.
- Binary is 1001000.
9. 101
For 101:
- Division gives remainders: 1 -> 0 -> 1 -> 0 -> 1.
- Binary is 1100101.
10. 120
Convert 120:
- Divide for bits: 0 -> 0 -> 1 -> 1 -> 1.
- Binary is 1111000.
11. 89
Convert 89:
- Calculate remainders: 1 -> 0 -> 1 -> 1 -> 0 -> 1.
- Binary is 1011001.
12. 194
Convert 194:
- Divide, noting remainders: 0 -> 1 -> 0 -> 0 -> 0 -> 1 -> 1.
- Binary is 11000010.
Each quotient division step helps us write the binary equivalent by reading from bottom up, compiling each remainder into the final binary number. These are your base ten numbers converted into base two (binary).
