Binary
From Compsci1
| Line 12: | Line 12: | ||
For example, | For example, | ||
| - | 00011010 + 00001100 = 00100110 | + | 00011010 + 00001100 = 00100110 |
| + | |||
1 1 carries | 1 1 carries | ||
| Line 19: | Line 20: | ||
+ 0 0 0 0 1 1 0 0 = 12(base 10) | + 0 0 0 0 1 1 0 0 = 12(base 10) | ||
| - | -------------------------------------------------------------------------------- | + | <nowiki>--------------------------------------------------------------------------------</nowiki> |
Revision as of 20:06, 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 0 1 10 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 0 1 1 0 10 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
