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# 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 8 bit 01001001
62 = 32+16+8+4+2+0 = 111110. In 8 bit 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.


# Revision

1.

 subtract 00101100 from 01001011 Using Two's compliment, write your answer as a Two's compliment binary integer. → First you find the first 1 (right to left) of the binary figure you are subtracting (00101100) and invert all the ones to zeros and zeros to ones to the left of the first one giving you 11010100. Next you add your new binary number to the binary number being subtracted from (01001011), this gives you an output of 100011111. Then since two's compliment is eight bit you have to disregard the ninth bit turning your nine bit answer to an eight bit answer (00011111) the correct final answer.

2.

 Using Two's compliment work out 107 - 49, give your answer as a two's compliment binary integer. → First you convert 107 and 49 to binary giving 01101011 and 00110001 respectively. then you convert 00110001 to a negative by inverting all figures after the first one right to left giving 11001111. then you add the two binary figures 01101011 and 11001111 giving 100111010, this answer is nine bit so you disregard the first bit making it the eight bit number 00111010, the correct answer.

3.

 Using Two's compliment work out 52 - 87, give your answer as a two's compliment binary integer. → First you convert 52 and 87 to binary giving 00110100 and 01001101 respectively. Then you convert 87 (01001101) to a negative by inverting all figures after the first 1 on the right giving 10110011. Then you add the two binary figures 00110100 and 10110011 giving 11100111.

4.

 Using Two's compliment work out 63 - 14, give your answer as a two's compliment binary integer. → First you convert 63 and 14 to binary giving 00111111 and 00001110 respectively. Then you convert 14 (00001110) to a negative by inverting all figures after the first 1 on the right giving 11000001. Then you add the two binary figures 00111111 and 11000001 giving 00110001.

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