Convert 103 base 10 to base 2,base 8, base 16
Base 2:
103 = 102 + 1
102/2 = 51
51 = 50 + 1
50/2 = 25
25 = 24 + 1
24/2 = 12
12/2 = 6
6/2 = 3
3 = 2 + 1
2/2 = 1
So, 103 in the binary system is:
1100111
To convert to base 8 you just take together 3 digits of the binary represenation together, to convert to base 16 you take together 4 digits.
Base 8:
1100111 ---> (001)(100)(111) =
(1)(4)(7) = 147
Base 16:
1100111 = (0110)(0111) = (6)(7) = 67
To convert a decimal number to different bases (base 2, base 8, and base 16), you need to divide the decimal number by the desired base repeatedly and record the remainders until the quotient becomes zero. Here's how you can convert 103 from base 10 to base 2, base 8, and base 16:
1. Converting to base 2 (binary):
To convert to base 2, divide the number 103 by 2 repeatedly until the quotient becomes zero, and record the remainder at each step. Finally, write the remainders in reverse order to get the base 2 representation.
```
Step 1: 103 ÷ 2 = 51 Remainder 1
Step 2: 51 ÷ 2 = 25 Remainder 1
Step 3: 25 ÷ 2 = 12 Remainder 1
Step 4: 12 ÷ 2 = 6 Remainder 0
Step 5: 6 ÷ 2 = 3 Remainder 0
Step 6: 3 ÷ 2 = 1 Remainder 1
Step 7: 1 ÷ 2 = 0 Remainder 1
The base 2 representation of 103 is 1100111.
```
2. Converting to base 8 (octal):
To convert to base 8, follow the same process as in base 2, but divide by 8 instead of 2.
```
Step 1: 103 ÷ 8 = 12 Remainder 7
Step 2: 12 ÷ 8 = 1 Remainder 4
Step 3: 1 ÷ 8 = 0 Remainder 1
The base 8 representation of 103 is 147.
```
3. Converting to base 16 (hexadecimal):
To convert to base 16, divide the number 103 by 16 repeatedly until the quotient becomes zero, and record the remainder at each step. Use the symbols A, B, C, D, E, and F to represent values greater than 9.
```
Step 1: 103 ÷ 16 = 6 Remainder 7
The base 16 representation of 103 is 67 in hexadecimal.
```
So, the decimal number 103 in base 10 can be expressed as 1100111 in base 2, 147 in base 8, and 67 in base 16.