Binary
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1 + 1 = 0, and carry 1 to the next more significant bit | 1 + 1 = 0, and carry 1 to the next more significant bit | ||
| + | |||
For example, | For example, | ||
00011010 + 00001100 = 00100110 | 00011010 + 00001100 = 00100110 | ||
| - | + | 1 1 carries | |
| - | 0 0 0 1 1 0 1 0 = 26(base 10) | + | 0 0 0 1 1 0 1 0 = 26<sub>(base 10)</sub> |
| - | 0 0 0 0 1 1 0 0 = 12(base 10) | + | 0 0 0 0 1 1 0 0 = 12<sub>(base 10) </sub> |
+ | + | ||
| - | + | -------------------------------------------------------------------------------- | |
| - | 0 0 1 0 0 1 1 0 = 38(base 10) | + | 0 0 1 0 0 1 1 0 = 38<sub>(base 10) </sub> |
| Line 31: | Line 32: | ||
00010011 + 00111110 = 01010001 | 00010011 + 00111110 = 01010001 | ||
| - | + | 1 1 1 1 1 carries | |
| - | + | 0 0 0 1 0 0 1 1 = 19<sub>(base 10) </sub> | |
| - | + | 0 0 1 1 1 1 1 0 = 62<sub>(base 10) </sub> | |
| + | + | ||
| - | + | ---------------------------------------------------------------------- | |
| - | 0 1 0 1 0 0 0 1 = 81(base 10) | + | 0 1 0 1 0 0 0 1 = 81<sub>(base 10)</sub> |
| - | + | ||
==Rules of Binary Subtraction== | ==Rules of Binary Subtraction== | ||
0 - 0 = 0 | 0 - 0 = 0 | ||
| + | |||
0 - 1 = 1, and borrow 1 from the next more significant bit | 0 - 1 = 1, and borrow 1 from the next more significant bit | ||
| + | |||
1 - 0 = 1 | 1 - 0 = 1 | ||
| + | |||
1 - 1 = 0 | 1 - 1 = 0 | ||
| + | |||
For example, | For example, | ||
00100101 - 00010001 = 00010100 | 00100101 - 00010001 = 00010100 | ||
| - | |||
| - | |||
| - | |||
| - | - | + | 0 borrows |
| - | + | ||
| + | 0 0 <strike>1</strike> <sup>1</sup>0 0 1 0 1 = 37<sub>(base 10) </sub> | ||
| + | |||
| + | 0 0 0 1 0 0 0 1 = 17<sub>(base 10)</sub> | ||
| + | |||
| + | - | ||
| + | |||
| + | ------------------------------------------------------------- | ||
| + | |||
| + | 0 0 0 1 0 1 0 0 = 20<sub>(base 10)</sub> | ||
00110011 - 00010110 = 00011101 | 00110011 - 00010110 = 00011101 | ||
| - | + | 0 <sup>1</sup>0 1 borrows | |
| - | + | ||
| - | + | 0 0 <strike>1 1 0 </strike><sup>1</sup>0 1 1 = 51<sub>(base 10)</sub> | |
| + | |||
| + | 0 0 0 1 0 1 1 0 = 22<sub>(base 10)</sub> | ||
| + | |||
| + | - | ||
-------------------------------------------------------------------------------- | -------------------------------------------------------------------------------- | ||
| - | + | 0 0 0 1 1 1 0 1 = 29<sub>(base 10)</sub> | |
Current revision as of 20:31, 1 October 2006
a good resource on Binary
Rules of Binary Addition
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 0, and carry 1 to the next more significant bit
For example,
00011010 + 00001100 = 00100110
1 1 carries
0 0 0 1 1 0 1 0 = 26(base 10)
0 0 0 0 1 1 0 0 = 12(base 10)
+
0 0 1 0 0 1 1 0 = 38(base 10)
00010011 + 00111110 = 01010001
1 1 1 1 1 carries
0 0 0 1 0 0 1 1 = 19(base 10)
0 0 1 1 1 1 1 0 = 62(base 10)
+
0 1 0 1 0 0 0 1 = 81(base 10)
Rules of Binary Subtraction
0 - 0 = 0
0 - 1 = 1, and borrow 1 from the next more significant bit
1 - 0 = 1
1 - 1 = 0
For example,
00100101 - 00010001 = 00010100
0 borrows
0 0110 0 1 0 1 = 37(base 10)
0 0 0 1 0 0 0 1 = 17(base 10)
-
0 0 0 1 0 1 0 0 = 20(base 10)
00110011 - 00010110 = 00011101
0 10 1 borrows
0 01 1 010 1 1 = 51(base 10) 0 0 0 1 0 1 1 0 = 22(base 10)
-
0 0 0 1 1 1 0 1 = 29(base 10)
Notes
Binary Number System
System Digits: 0 and 1
Bit (short for binary digit): A single binary digit
LSB (least significant bit): The rightmost bit
MSB (most significant bit): The leftmost bit
Upper Byte (or nybble): The right-hand byte (or nybble) of a pair
Lower Byte (or nybble): The left-hand byte (or nybble) of a pair
Binary Equivalents
1 Nybble (or nibble) = 4 bits
1 Byte = 2 nybbles = 8 bits
1 Kilobyte (KB) = 1024 bytes
1 Megabyte (MB) = 1024 kilobytes = 1,048,576 bytes
1 Gigabyte (GB) = 1024 megabytes = 1,073,741,824 bytes
