Decimal.
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
In the decimal number system, the third place to the left of the decimal point is the hundreds place, and note that this is true even if you have not written in any actual decimal point. For example, one hundred is written as 100 with the digit 1 in the third place left of the decimal. We can imagine it as 100. but we would normally use the decimal only if there was an actual fraction involved. Money is a very good example of the use of decimal points. Let us say that your new coat costs $129.99 which means, one hundred and twenty nine dollars and ninety nine cents. Every number has a particular place, in relation to the decimal point. But even if the coat cost exactly $129 we know that we can still write in a decimal point, after the 9. That's where it goes.
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.
In terms of day to day business, the binary number system holds no real advantage in the business world over decimal. The binary number system is merely another means of representing numbers; akin to another language if you will. You can do the same operations in base 2 (binary) as base 10 (regular decimal) without losing any precision or inserting any errors. The advantage of base 10 is that people are taught to think on base 10. Everybody knows 2 + 2 = 4. Few know 0b10 + 0b10 = 0b100. (Note the use of the 0b prefix to signify binary.) Where base 2 really holds it's own is in digital computing systems. In a digital system a data line is either on or off, 1 or 0. You cannot represent a base 10 digit on a single dateline. To directly represent a base 10 number digitally you need four datelines per digit. (This is known as Binary Coded Decimal.) However, this method is wasteful as 4 binary digits can store 0-15 but is only being used for 0-10. Also, because of that discontinuity special circuitry is required. With binary, the full range of the data bus (2 ^ (number of lines (bits)) can be utilized. Half-adders can be used for adding, and the twos-compliment method for storing negative numbers can be used which allows for subtraction using half-adders. Binary allows digital systems to operate. This, however, is unseen to most business people as knowledge of exactly how a calculator works is not requisite to use one. I'll sum up with an old joke: There are 10 kinds of people in the world: Those who understand binary and those who don't.
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.
To convert the binary number 1010 to decimal, we start from the right and assign each digit a power of 2, increasing from right to left. In this case, the rightmost digit is 0, so it has no contribution. Moving left, the next digit is 1, which corresponds to 2^1. The next digit is also 0, so it has no contribution. The leftmost digit is 1, which corresponds to 2^3. Adding these contributions together (0 + 2 + 0 + 8) gives us the decimal equivalent of 1010, which is 10.
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.