Decimal.
The US system that is based on the number 10 is the base 10 system. In the base 10 system the numbers roll over every 10; example 10,20,30.
The number 100010000001000000 is 100,010,000,001,000,000 which is (short scale, US) 100 quadrillion, 10 trillion, and 1 million. Decimally, this is 1.00010000001 x 1017 or [ 1 x 1017 + 1 x 1013 + 1 x 106 ] If the number is a binary number it is equivalent to 139,328 in decimal
There is no such thing as a binary encoded hexadecimal value. The encoding is simply the representation of a number. E.g., the symbol 42 is not a number, it is merely the representation of a number. Forty-two is an actual number. This is because 42 is only the number forty-two when the digits are base-10 (decimal). In octal notation, 42 is thirty-four and in hexadecimal notation 42 is sixty-six. Humans use decimal encoding to represent numbers simply because that's the way we were taught from an early age. We consider them easy to work with simply because we consider it easier to work in powers of 10. However, it's really no easier than working in powers of 5 or 12. Before decimalisation became the norm we actually used sexagesimal, base-60, because of its high divisibility (it's the lowest number that has all the factors 2, 3, 4, 5 and 6). Hence there are 60 seconds to the minute, 60 minutes to the hour, 24 hours in the day (2x2x2x3) and 360 degrees in a rotation. Binary and hexadecimal are simply different ways of encoding the same number. Computers only understand binary, but binary notation is tedious for humans because there are only two symbols to work with. Higher bases allow us to work with numbers more quickly because there are more symbols to play with and therefore more values we can represent with just a single digit. However, any base that is itself a power of two gives us a very simple conversion to and from binary. That is; base-4, base-8 and base-16 are more closely related to binary than is decimal. For instance, two binary digits have four possible combinations, each of which can be represented by just one base-4 digit. Three binary digits have eight possible combinations each of which can be represented by just one base-8 digit (octal notation). It therefore follows that a single base-16 digit can represent any combination of 4-bits. Since a byte is typically 8-bits in length, a hexadecimal digit is known as nybble because it is half-a-byte. Knowing this we can easily convert any number from hexadecimal to binary and back again. And if we can do it easily then a computer can do it just as easily. Converting to and from decimal is not so straightforward, but the computer can be programmed to do that for us as well, since decimal is the notation we're more used to. But when we want to instruct the computer in its own language, hexadecimal is easier to work with than decimal.
At first sight this looks as if it already is binary. If you need something to be converted from one base to another you need to tell us what base it's in now and what you would like it to be converted to.
Decimal.
Nowadays the whole world uses the same number system - decimal for daily use and (essentially) binary for electronic and optical data storage and processing.
Decimal
A decimal number is simply a way of representing a number in such a way that the place value of each digit is ten times that of the digit to its right.
The US system that is based on the number 10 is the base 10 system. In the base 10 system the numbers roll over every 10; example 10,20,30.
1 and 0 stands in for both of these states. Binary numerals are composed of the numbers 1 and 0. Different data are represented by these numbers. The number system is commonly referred to as binary, or base 2 because numbers are represented by two digits.
Binary numbers have the virtue of being simple enough that they can be represented by a purely physical system, in which a magnetic north pole can represent (let us say) a 1, and a magnetic south pole can represent a 0, or a current being on can represent a 1 and the same current being off can represent a 0. In other words, the physical world contains analogs of binary systems. If you wanted to use decimal numbers you would have to find a physical system that has ten variables, which are relatively easy to measure and to create as needed, and that is not going to be easy.
11001. To convert a decimal number to binary, we start with the highest power of two that goes into the decimal number once, and reduce from there. For 25, we move forward as follows: 25 is first divisible by 16, so we get 1 and are left with 9 After 16, we check to see 8 and 9 can be divided by eight, getting us another 1 After 8, we are left with 1. 1 cannot be divided by 4 or 2, so we get two 0s. Finally 1 is divisible by 1, giving us a 1. Stringing what we found together, we get the following 1 1 0 0 1.
The number 100010000001000000 is 100,010,000,001,000,000 which is (short scale, US) 100 quadrillion, 10 trillion, and 1 million. Decimally, this is 1.00010000001 x 1017 or [ 1 x 1017 + 1 x 1013 + 1 x 106 ] If the number is a binary number it is equivalent to 139,328 in decimal
Binary is a base 2 number system, while octal is base 8. This happens to make conversion between binary and octal fairly trivial, although more complex than conversion to hexadecimal. To convert to octal from binary, take each three bits, starting from the least significant bit, and convert them to their octal equivalent. Examples: 25510 = 111111112 = 11 111 111 = 3778 17410 = 101011102 = 10 101 110 = 2568 You can repeat this process for as many bits as you need. A 24-bit number should translate into 8 octal numbers, for reference.
Binary system is invented to allow its use for computers where "on" is for one and "off" is for zero. So, numbers could be easily identified by the computers.
Jefferson designed a decimal system for weights and measures which was proposed to Congress before the metric system (The SI system) which is now used throughout the world. He also devised a decimal system for the currency based on the Spanish dollar. The former was rejected by Congress and the US stuck to the clumsy British system, adding some further problems by redefining a gallon and so on. The US is one of a handful of countries still stuck with the Imperial system though it did adopt the decimal currency in 1792.