Subtraction

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.

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.

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