563 base 8 is 000101110011 in binary.
300 = 256 + 32 + 8 + 4 = Binary 0000 0001 0010 1100
262,144 = 2.62144 x 10^5262144 is standard notation for 86 (exponential notation), where 8 is the base and 6 is the exponent.
It is not. "Scientific notation" uses a base of 10. The correct notation would be 1.251 x 10^8
You cannot know that. It could be base 10.
1001 (base 2) = 1(2)3 + 0 + 0 + 1 = 8 + 1 = 9 (base 10)9 (base 10) = 1(8) + 1 = 11 (base 8).
Decimal is base 10. Binary is base 2. Octal is base 8. Hexadecimal is base 16.
The binary number 1000 is the decimal (base 10) number 8. The digits in a binary number are exponents of 2 rather than 10, so that for a four-digit number in binary, the digit places represent 8, 4, 2, 1 1000 (binary) = 8 + (0x4) + (0x2) + (0x1) = 8
70.375
500 + 60 + 3 + 0.8 + 0.04
300 = 256 + 32 + 8 + 4 = Binary 0000 0001 0010 1100
14 decimal in binary is 11102. In octal it is 168 and in hexadecimal it is 0E16.
Any base that is itself a power of 2 can be used to notate binary values. That is, base-4, base-8 (octal), base-16 (hexadecimal), base-32, and so on. Binary is a base-2 counting system such that each digit represents one of two possible values (0 or 1). When we combine bits we double the number of possible values with each additional bit. Thus 2 bits can represent up to 4 possible values, 3 bits gives us 8 possible values and 4 bits gives us 16 possible values, and so on. We normally deal with bits in groups of 4 because 2 groups of 4 gives us an 8-bit byte which is the norm for most systems. Thus we can reduce an 8-bit binary value from 8 binary digits to just 2 hexadecimal digits, thus giving us a convenient method of notating binary values with fewer digits and a trivial conversion. Octal notation isn't used as much as hexadecimal notation, but if we wanted to use a 9-bit byte rather than an 8-bit byte (which is not an uncommon activity), octal notation is more convenient than hexadecimal because the 9-bit values can be treated as being exactly 3 groups of 3 bits.
262144 is standard notation for 8⁶, where 8 is the base and 6 is the exponent
It is not. "Scientific notation" uses a base of 10. The correct notation would be 1.251 x 10^8
262,144 = 2.62144 x 10^5262144 is standard notation for 86 (exponential notation), where 8 is the base and 6 is the exponent.
262144 is standard notation for 86 (which is your exponential notation). Here 8 is your base and 6 is your exponent.
The connection between binary and hexadecimal in the programming world is exactly the same as the connection in the mathematical world. All numeric bases that are themselves a power of 2 (base-4, base-8, base-16, base-32, etc) are trivial to convert both to and from binary. A single base-4 digit maps to exactly 2 binary digits: 0 = 00 1 = 01 2 = 10 3 = 11 A single base-8 (octal) digit maps to exactly 3 binary digits: 0 = 000 1 = 001 2 = 010 3 = 011 4 = 100 5 = 101 6 = 110 7 = 111 A single base-16 (hexadecimal) digit maps to exactly 4 binary digits (also known as a nybble): 0 = 0000 1 = 0001 2 = 0010 3 = 0011 4 = 0100 5 = 0101 6 = 0110 7 = 0111 8 = 1000 9 = 1001 a = 1010 b = 1011 c = 1100 d = 1101 e = 1110 f = 1111 And so on for base-32, base-64, etc. Hexadecimal is the most useful notation because a byte is normally 8 binary digits in length and we can represent a byte as two nybbles using just two hexadecimal digits as opposed to 8 binary digits. For longer binary values, such as 32-bit, 64-bit or 128-bit values, using a more concise notation makes the value much easier to read. Consider the following: 1011010010110100101101001011010010110100101101001011010010110100 1011010010110100101111001011010010110100101101001011010010110100 These two binary values look the same but they are not. With hexadecimal notation it becomes easier to see the difference because there are fewer digits to compare: b4b4b4b4b4b4b4b4 b4b4bcb4b4b4b4b4