1-20Now let’s look at the number system that most computers use, the binary system. Just as the decimalsystem, had the nines (R’s-1) and tens (R’s) complement, the binary system has two types of complementmethods. These two types are the ones (R’s-1) complement and the twos (R’s) complement. The binarysystem R’s-1 complement is the difference between the binary number and all 1s. The R’s complement isthe difference between the binary number and the next higher power of 2.Let’s look at a quick and easy way to form the R’s-1 complement. To do this, change each 1 in theoriginal number to 0 and each 0 in the original number to 1 as has been done in the example below.1011011_{2}100100_{2} R’s-1 complementThere are two methods of achieving the R’s complement. In the first method we perform the R’s-1complement and then add 1. This is much easier than subtracting the original number from the next higherpower of 2. If you had subtracted, you would have had to borrow.Saying it another way, to reach the R’s complement of any binary number, change all 1s to 0s and all0s to 1s, and then add 1.As an example let’s determine the R’s complement of 10101101_{2}:The second method of obtaining the R’s complement will be demonstrated on the binary number00101101100_{2}.Step 1—Start with the LSD, working to the MSD, writing the digits as they are up to and includingthe first one.

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