Q&A for How to Convert from Binary to Decimal

First, ignore the decimal sign and keep dividing the number by 2 until the quotient is 0, always writing down the remainder to the right of each quotient. Write down the remainders from bottom to top of the list to make a sequence of 1s and 0s, and divide the list up into groups of 4, starting at the end. Add extra 0s to the front of the list if you have to. To convert the binary representation into a negative number, “flip” the sequence so that each 0 becomes a 1 and each 1 becomes a 0. Add 1 to the sequence to get your final answer. Remember that 1 + 1 = 10 in binary.

Yes. Binary is base 2, while hexadecimal is base 16. Hexadecimal numbers can be represented as the numbers 0-9 and the letters A-F (for numbers greater than 10). You’ll need to take a binary line of 4 numbers and multiply the numbers by 1, 2, 4, and 8, respectively, going from right to left. Add the results together to get your answer.

1x2^4 + 1x2^3 + 1x2^2 + 0x2^1 + 0x2^0 + 1x2^-1 + 0x2^-2 + 1x2^-3 + 0x2^-4 = 29.6250

It actually doesn't get any simpler than what is shown above.

If you're using small numbers, like below 256, you can easily figure it out without much of a technique. Just take a number like 50: The binary system is 128 64 32 16 8 4 2 1. Work from left to right checking if the number of the binary system will fit into your number, so the first would of 32 for 50. From this we know the start of the binary number: 001. If you take away 32 from 50 you will get 18, which will need to be formed from the remaining binary number, so check from left to right again, and you find that 16 fits in, so the start of the number is 0011, and we have 2 left over, so we can find the binary number as 0011 0010.

It's a convenient way to help prevent confusion when working with bases other than ten.

The base value is always 2 in binary, as there are 2 numbers used in the system. In decimal, 10 numbers are used, so 10 is the base value.

If D2 = decimal 2, then the binary would be 10 with base 2. If D2 = hexidecimal, then the binary would be 11010010 with base 2.

By reversing the rules above, you get 01000000.

It is a prefix that helps a computer identify what base the digits are in. Here are a few examples: "0b" = binary form, "0x" = hexadecimal, "0d" = denary.

Multiply the positional value (1, 2, 4, 8, etc.) by the digit (0 or 1) in that position. You do the same thing with numbers in base-ten or any other base.

It is 46. 101110 = (1 × 2⁵) + (0 × 2⁴) + (1 × 2³) + (1 × 2²) + (1 × 2¹) + (0 × 2⁰) = 46.

Yes. It should be, and the next line is also wrong. Both times the 38 should be 39. The final answer of 1446 is correct because it's 39*37 + 3.

Using powers of 2, we get 1x2^6 + 0x2^5 + 1x2^4 + 1x2^3 + 1x2^2 + 1x2^1 + 1x2^0 = 64+0+16+6+4+2+1 = 95 in decimal. Using doubling, we get: 0x2+1 = 1; 1x2+0 = 2; 2x2+1 = 5; 5x2+1 = 11; 11x2+1 = 23; 23x2+1 = 47; 47x2+1 = 95, which is the same as the powers of 2 method.

Yes, there is a mistake on the diagram. It should be: 0x37+1=1. 1x37+2=39. 39x37+3=1446. 123 base 37 = 1446 base 10.

For unsigned integers, It is 2n-1, where n is the number of bits in the binary number. So for 16 bits, it is 1111 1111 1111 1111 = 65536 - 1 = 65535. For 32 bits, it is 232-1 = 4,294,967,296 - 1 = 4,294,967,295. For 64 bits, it is 232-1 = 18,446,744,073,709,551,616 - 1 = 18,446,744,073,709,551,615. For signed integers, the largest positive number is 2n-1 -1. We have n-1 bits because the highest bit is used for negative numbers, and we count the 0s instead of the 1s. This is called 2's complement notation. The smallest negative number is then 2n-1 * -1. For 32 bits, we get 2,147,483,647 and -2,147,483,648, respectively.