Hexadecimal: Difference between revisions
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(Extended, including conversions from bin to hex without decimal.) |
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[[Category:Encyclopedia]]Hexadecimal |
[[Category:Encyclopedia]]Hexadecimal is a counting system that uses sixteen digits. |
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Instead of using only 0's and 1's like binary, or 0 |
Instead of using only 0's and 1's like binary, or the characters 0 to 9 of the decimal number system; hexadecimal uses the characters '0' to '9' to represent the numbers 0 to 9, and also the single characters 'A' to 'F' (or sometimes 'a' to 'f', but usually not mixing case), to represent the numbers 10 through to 15, in order. |
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== Uses == |
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Ex. |
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The hexadecimal number system is used widely in the Electronics and Computer Industry, as although digital electronics is based on gates with only two states and is therefore fundamentally binary, binary numbers can quickly become long and hard to transcribe without errors. Their hexadecimal equivalents are much shorter and easier to remember, and have a straight-forward way of conversion to/from binary. |
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10010111 |
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== Comparing counts from zero in different number systems == |
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2^3+2^0 2^2+2^1+2^0 |
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Binary |
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Decimal |
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Hexadecimal |
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0 0 0 |
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1 1 1 |
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10 2 2 |
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11 3 3 |
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100 4 4 |
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101 5 5 |
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110 6 6 |
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111 7 7 |
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1000 8 8 |
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1010 10 A |
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1011 11 B |
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1100 12 C |
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1101 13 D |
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1110 14 E |
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1111 15 F |
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10000 16 10 |
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10001 17 11 |
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10010 18 12 |
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10011 19 13 |
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10100 20 14 |
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10101 21 15 |
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10110 22 16 |
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10111 23 17 |
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11000 24 18 |
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11001 25 19 |
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11010 26 1A |
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11011 27 1B |
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11100 28 1C |
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11101 29 1D |
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11110 30 1E |
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11111 31 1F |
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100000 32 20 |
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100001 33 21 |
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== Converting binary to hexadecimal == |
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# Split a binary number into groups of four digits, counting from right to left. |
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# Pad the leftmost group of binary digits with zeros on their left if their are less than four digits. |
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# Use the following table to translate each group of four binary digits, in order, to its hexadecimal equivalent. |
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Binary digits |
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Hexadecimal equivalent digit |
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0000 0 |
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0001 1 |
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0010 2 |
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0011 3 |
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0100 4 |
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0101 5 |
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0110 6 |
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0111 7 |
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1000 8 |
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1001 9 |
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1010 A |
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1011 B |
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1100 C |
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1101 D |
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1110 E |
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1111 F |
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=== An example conversion === |
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Binary Number: 1011010111 |
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Split: 10 1101 0111 |
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Pad: 0010 1101 0111 |
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Translate groups: 2 D 7 |
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Hexadecimal answer: 2D7 |
Revision as of 04:43, 31 January 2009
Hexadecimal is a counting system that uses sixteen digits.
Instead of using only 0's and 1's like binary, or the characters 0 to 9 of the decimal number system; hexadecimal uses the characters '0' to '9' to represent the numbers 0 to 9, and also the single characters 'A' to 'F' (or sometimes 'a' to 'f', but usually not mixing case), to represent the numbers 10 through to 15, in order.
Uses
The hexadecimal number system is used widely in the Electronics and Computer Industry, as although digital electronics is based on gates with only two states and is therefore fundamentally binary, binary numbers can quickly become long and hard to transcribe without errors. Their hexadecimal equivalents are much shorter and easier to remember, and have a straight-forward way of conversion to/from binary.
Comparing counts from zero in different number systems
Binary Decimal Hexadecimal 0 0 0 1 1 1 10 2 2 11 3 3 100 4 4 101 5 5 110 6 6 111 7 7 1000 8 8 1001 9 9 1010 10 A 1011 11 B 1100 12 C 1101 13 D 1110 14 E 1111 15 F 10000 16 10 10001 17 11 10010 18 12 10011 19 13 10100 20 14 10101 21 15 10110 22 16 10111 23 17 11000 24 18 11001 25 19 11010 26 1A 11011 27 1B 11100 28 1C 11101 29 1D 11110 30 1E 11111 31 1F 100000 32 20 100001 33 21
Converting binary to hexadecimal
- Split a binary number into groups of four digits, counting from right to left.
- Pad the leftmost group of binary digits with zeros on their left if their are less than four digits.
- Use the following table to translate each group of four binary digits, in order, to its hexadecimal equivalent.
Binary digits Hexadecimal equivalent digit 0000 0 0001 1 0010 2 0011 3 0100 4 0101 5 0110 6 0111 7 1000 8 1001 9 1010 A 1011 B 1100 C 1101 D 1110 E 1111 F
An example conversion
Binary Number: 1011010111 Split: 10 1101 0111 Pad: 0010 1101 0111 Translate groups: 2 D 7 Hexadecimal answer: 2D7