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Why is it easier to convert numbers from binary to hexadecimal than decimal to hexadecimal?
Wiki User
∙ 8y ago
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
Wiki User
∙ 14y ago
Wiki User
∙ 8y agoEach hexadecimal digit can hold one of 16 values (0-F); 16 = 2^4, so exactly 4 bits (binary digits) can hold the same value as 1 hexadecimal digit. As a result the conversion from binary to hexadecimal is simply a matter of grouping the bits together in blocks of 4 (making nybbles) and converting each block into a single hexadecimal digit. Similarly for binary to octal but in this case as 8 = 2³ the bits are group into blocks of 3 which are then converted into octal digits.
However, converting decimal to hexadecimal is not so "easy" as each decimal digit does not map to an exact number of binary digits. The only exception would be when using BCD (Binary Coded Decimal) where only the bit patterns for the decimal digits 0-9 are used in every 4 bits (wasting 6 possible digits) and where 0000 1001 (09) + 0000 0001 (01) = 0001 0000 (10). In this case the hexadecimal representation of the BCD is exactly the same as the decimal, but I have never seen it used as such (beyond the binary representation).
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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.
What is the 4-binary number assoiated with the hexadecimal symbol C?
0xc = 1100 Hexadecimal digits use exactly 4 binary digits (bits). The 0x0 to 0xf of hexadecimal map to 0000 to 1111 of binary. Thinking of the hexadecimal digits as decimal numbers, ie 0x0 to 0x9 are 0 to 9 and 0xa to 0xf are 10 to 15, helps with the conversion to binary: 0xc is 12 decimal which is 8 + 4 → 1100 in [4 bit] binary.
Why people are using Hexadecimal rather than binary numbers while doing programs?
hexadecimal can express 16 bit binary in 4 place form, not 16.
Write a program that prints a table of the binary octal and hexadecimal equivalents of the decimal numbers in the range 1 through to 256?
import java.util.Scanner; public class NumberSystem { public void displayConversion() { Scanner input = new Scanner(System.in); System.out.printf("%-20s%-20s%-20s%-20s\n", "Decimal", "Binary", "Octal", "Hexadecimal"); for ( int i = 1; i <= 256; i++ ) { String binary = Integer.toBinaryString(i); String octal = Integer.toOctalString(i); String hexadecimal = Integer.toHexString(i); System.out.format("%-20d%-20s%-20s%-20s\n", i, binary, octal, hexadecimal); } } // returns a string representation of the decimal number in binary public String toBinaryString( int dec ) { String binary = " "; while (dec >= 1 ) { int value = dec % 2; binary = value + binary; dec /= 2; } return binary; } //returns a string representation of the number in octal public String toOctalString( int dec ) { String octal = " "; while ( dec >= 1 ) { int value = dec % 8; octal = value + octal; dec /= 8; } return octal; } public String toHexString( int dec ) { String hexadecimal = " "; while ( dec >= 1 ) { int value = dec % 16; switch (value) { case 10: hexadecimal = "A" + hexadecimal; break; case 11: hexadecimal = "B" + hexadecimal; break; case 12: hexadecimal = "C" + hexadecimal; break; case 13: hexadecimal = "D" + hexadecimal; break; case 14: hexadecimal = "E" + hexadecimal; break; case 15: hexadecimal = "F" + hexadecimal; break; default: hexadecimal = value + hexadecimal; break; } dec /= 16; } return hexadecimal; } public static void main( String args[]) { NumberSystem apps = new NumberSystem(); apps.displayConversion(); } }
What is the decimal equivalent of 0XFFFF?
0X at the beginning represent a number in the hexadecimal system of units. FFFF is the hexadecimal equivalent of i) 65535 in decimal system of units ii) 1111111111111111 in binary system of units
Convert 110001100 into its decimal numbers?
The answer depends on what you are converting from: binary, ternary, octal, hexadecimal ...
Convert hexadecimal 4F7B in to binary and decimal?
4F7B: Binary = 100111101111011 Decimal = 20347
Why is Hexadecimal used?
It is used because it is easier to convert to and from binary to hexadecimal than decimal, and it uses less characters than binary. For instance: decimal: 65535 hex: FFFF binary: 1111111111111111
Convert the hexadecimal number 221122 into binary octal and decimal?
221122: Binary = 1000100001000100100010 Octal = 10410442 Decimal = 2232610
Convert 11011001 to decimal?
The answer depends on what you are converting from: binary, ternary, octal, hexadecimal ...
Why is it impossible to convert a decimal number to binary on a digit by digit basis as can be done for Hexadecimal?
Because - Hex is an exact multiple of binary - whereas decimal numbers need to be converted from base 10 to base 2.
Convert the following decimal numbers into their equivalent binary numbers and then convert the resulting binary numbers back into the decimal numbers a. 6401 b. 1010110?
a) 6401 in Binary is 1100100000001b) 1010110 in decimal is 86
Why do we use decimal prime numbers?
Prime numbers are prime numbers - whether we count in the decimal, binary, hexadecimal or another base.
Why is it more difficult to convert decimal to hexadecimal?
As compared to converting decimal into what other base! It is no more difficult to convert decimal into base 8 than decimal into binary or Hex.
Convert 186 decimal numbers to its binary equivalent?
Convert 189 to binary number
Which utility in XP converts numbers from decimal to hexadecimal?
Excel (not an XP utility but part of the MS Office suite that runs on XP) can convert these.The Calculator (calc.exe) that ships with XP is capable of converting between Decimal, Binary, Octal and Hexadecimal.
What does one use a hex converter for?
A hex converter is used to convert hexadecimal numbers to binary or decimal numbers, which is necessary for programming or studying computer science. Hex converters are usually online tools that will automatically convert the numbers for you quickly and easily.
