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Two numbers that have the same decimal value will have the same binary value. Binary is simply a representation of a number in base 2, while decimal is base 10.
For example, consider the number 104 in base 10. In this system, we can break down each digit due to the distributive law.
104 = 1 * (10^2) + 0 * (10^1) + 4 * (10^0) = 100 + 0 + 4 = 104
To convert to base 2, we can find the largest power of two that is less than our base 10 number and work backwards from there, in this case we start at 2^6 or 64
2^6 = 64
104 - 64 = 40
2^5 = 32
40 - 32 = 8
2^3 = 8
8 - 8 = 0
so therefore:
104 = 1 * (2^6) + 1 * (2^5) + 0 * (2^4) + 1 * (2^3) + 0 * (2^2) + 0 * (2^1) + 0 * (2^0)
meaning that 104 base 10 is equal to 1101000 base 2.
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What does hexadecimal base 16 convert binary equal?
16 is the 4th power of 2. So a hexadecimal number is converted to binary by replacing each hex digit by the 4-bit binary number having the same value. Conversely, in converting binary to hexadecimal, we group every 4 bits starting at the decimal (binary?) point and replace it with the equivalent hex digit. For example, the hexadecimal number 3F9 in binary is 1111111001, because 3 in binary is 11, F (decimal 15) is 1111, and 9 is 1001.
Why do computers work with bits rather than decimal digits?
Ever wonder what the real numbers are? Numbers are artificial things invented by human, and the same applied to computers. So, the inventors of computers storing human readable numbers (decimal, Roman numerals, etc...) as computer readable numbers (binary). Binary fit very well with the electrical pulses (on and off, as 1 and 0)
The binary number 00110110 is the decimal number?
The first digit is worth 20 (or 1), the second 21 (or 2), the third 22 (or 4), the fourth 23 (or 8), the fifth 24 (or 16), the sixth 25 (or 32) and so on. 001100 is thus 0x1 + 0x2 + 1x4 + 1x8 + 0x16 + 0x32 = 4 + 8 = 12
Why is it easier to convert numbers from binary to hexadecimal than decimal to hexadecimal?
A binary number system has two states '0' '1' for a long word in bits it can be as follows 101010101010101010101011 intimidating RIGHT? it can be represented in groups of 3 bits in octal 10/010/101/010/101/010/101/011= 22525253 digital or in group of 4 bits as 10/1010/1010/1010/1010/1010 = 2AAAAA 111 =7 octal 1111=f F in hexadecimal numbers 1000 =8 1010 =10 or A
What is binary in R programming?
Binary in R is the same as binary in any other programming language. The language doesn't actually change the meaning of binary any more than it can change the meaning of decimal, octal or hexadecimal. These are all symbolic representations (notations) for digital information. When we see the symbol 42 we instantly recognise it as the value forty-two because we automatically assume numeric symbols are always written in decimal notation. However, the computer represents the value forty-two as 00101010, which is the binary equivalent. In order to present the decimal value to the user, the computer must convert the value 00101010 to the string "42". This is achieved through binary division by ten (00001010 in binary) and taking the remainder: 00101010 / 00001010 = 00000100 r 00000010 00000100 / 00001010 = 00000000 r 00000100 The remainders are decimal 2 and 4 respectively. Now we convert each of these digits to their equivalent ASCII character code by adding 48 (binary 110000), which is the ASCII code for character '0': 00000010 + 00110000 = 00110010 00000100 + 00110000 = 00110100 We output these two ASCII character codes in reverse order, so we now have {00110100, 00110010} which is {52, 50} in decimal. ASCII character code 52 yields '4' while ASCII character code 50 yields '2', which gives us the complete string, "42", which can now be presented to the user. Converting the other way takes the user-input string "42" and stores the value 00101010: First, subtract character code '0' (48 decimal) from each character: 00110010 - 00110000 = 00000010 (50 - 48 = 2) 00110100 - 00110000 = 00000100 (52 - 48 = 4) Multiply each digit by increasing powers of 10: 00000010 * 00000001 = 00000010 (2 * 10^0 = 2) 00000100 * 00001010 = 00101000 (4 * 10^1 = 40) Finally, sum the products: 00000010 + 00101000 = 00101010 (2 + 40 = 42) If we wish to see the binary representation of an integer, R provides the Int2Bin function: >intToBin(42, 8) [1] "00101010" Here we've requested the binary equivalent of the decimal value 42 in 8-bit binary which, as we've already established, outputs the binary value 00101010.
