Difference between revisions of "Subtraction"
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Binary subtraction uses twos's complement and binary addition. For example if a question asks for 73-62 in binary you would convert +62 to -62 using two's complement and then do 73+(-62) using binary addition. | Binary subtraction uses twos's complement and binary addition. For example if a question asks for 73-62 in binary you would convert +62 to -62 using two's complement and then do 73+(-62) using binary addition. | ||
| − | First you would write out 73 and 62 in their respective binary forms using your preferred method and then add 0's to make them 8bit | + | First you would write out 73 and 62 in their respective binary forms using your preferred method and then add 0's to make them 8bit: |
73= 64+0+0+8+0+0+1 = 1001001. In 8bit 01001001 | 73= 64+0+0+8+0+0+1 = 1001001. In 8bit 01001001 | ||
62 =32+16+8+4+2+0 = 111110. In 8bit 00111110 | 62 =32+16+8+4+2+0 = 111110. In 8bit 00111110 | ||
| − | Then convert +62 to -62 using your preferred method ([[Negative Numbers]]) | + | Then convert +62 to -62 using your preferred method ([[Negative Numbers]]): |
-62 = 11000010 | -62 = 11000010 | ||
| − | Then use binary addition to add 73 and -62 | + | Then use binary addition to add 73 and -62: |
01001001 + | 01001001 + | ||
11000010 | 11000010 | ||
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However the addition left us with a carried 1 that makes the result 9bit, as two's complement uses 8bit we simply ignore the carried one making our final answer equal 00001011. | However the addition left us with a carried 1 that makes the result 9bit, as two's complement uses 8bit we simply ignore the carried one making our final answer equal 00001011. | ||
| − | We can check by converting to denary | + | We can check by converting to denary: |
| + | 00001011 = 8+2+1=11 and 73-62=11. | ||
Revision as of 08:39, 15 December 2016
Binary Subtraction
Binary subtraction uses twos's complement and binary addition. For example if a question asks for 73-62 in binary you would convert +62 to -62 using two's complement and then do 73+(-62) using binary addition.
First you would write out 73 and 62 in their respective binary forms using your preferred method and then add 0's to make them 8bit:
73= 64+0+0+8+0+0+1 = 1001001. In 8bit 01001001 62 =32+16+8+4+2+0 = 111110. In 8bit 00111110
Then convert +62 to -62 using your preferred method (Negative Numbers):
-62 = 11000010
Then use binary addition to add 73 and -62:
01001001 + 11000010 =100001011
However the addition left us with a carried 1 that makes the result 9bit, as two's complement uses 8bit we simply ignore the carried one making our final answer equal 00001011.
We can check by converting to denary:
00001011 = 8+2+1=11 and 73-62=11.
