What type of numbering system is binary? point) base 2 with only and base 3 with only , and 10s base 10 with 10 single -digit numbers through 9 base 16 with 10 single-digit numbers through 9 and the first 6 alphabet letters A through F
Binary is a numbering system that uses base 2, consisting only of 0s and 1s.
Binary is a numbering system that uses base 2, meaning it only has two distinct digits: 0 and 1. Each digit in a binary number represents a power of 2. In this system, numbers are expressed using only these two digits.
The numbering system you're referring to is called binary. Binary is a base-2 numbering system, which means it only uses two digits: 0 and 1. In binary, each digit represents a power of 2. The rightmost digit represents 2^0 (1), the next digit represents 2^1 (2), the next digit represents 2^2 (4), and so on. By combining these digits, you can represent any number using only 0s and 1s.
To convert a number from decimal (base-10) to binary (base-2), you can follow these steps:
1. Start with the decimal number you want to convert.
2. Divide the number by 2 and write down the remainder.
3. Divide the quotient (the result of the division) by 2 again and write down the remainder.
4. Repeat step 3 until the quotient becomes zero.
5. Write the remainders in reverse order to get the binary representation of the decimal number.
For example, let's convert the decimal number 10 to binary:
- Divide 10 by 2, we get a quotient of 5 and a remainder of 0.
- Divide 5 by 2, we get a quotient of 2 and a remainder of 1.
- Divide 2 by 2, we get a quotient of 1 and a remainder of 0.
- Divide 1 by 2, we get a quotient of 0 and a remainder of 1.
Writing down the remainders in reverse order, we get the binary representation of 10 as 1010.
Conversely, to convert a binary number to decimal, you can multiply each binary digit by the corresponding power of 2 and then add up the results.
For example, let's convert the binary number 1011 to decimal:
- The leftmost digit (1) represents 2^3 (8).
- The next digit (0) represents 2^2 (4).
- The next digit (1) represents 2^1 (2).
- The rightmost digit (1) represents 2^0 (1).
Adding up these values, we get 8 + 0 + 2 + 1 = 11. Thus, the binary number 1011 is equivalent to the decimal number 11.