3-11Now let’s subtract 10_{2} from 11_{2} using the adder/subtracter circuit. The minuend (11_{2}) is input on theA terminals, and the subtrahend (10_{2}) is input on the B terminals. In the subtract mode, a 1 from thecontrol circuit is input to each of the X-OR gates and to the C_{0} carry input. By applying a 1 to each of theX-OR gates, you find the output will be the complement of the subtrahend input at B_{1} and B_{2}. Since B_{1} isa 0, the output of X-OR 1 will be 1. The input B_{2} to X-OR 2 will be inverted to a 0. The HIGH input to C_{0}acts as a carry from a previous circuit. The combination of the X-OR gates and the HIGH at C_{0} producesthe R’s complement of the subtrahend. The full adders add the minuend and the R’s complement of thesubtrahend and produce the difference. The output of C_{2} is not used. The outputs of S_{2} and S_{1} are 0 and 1,respectively, indicating a difference of 01_{2}. Therefore, 11_{2} minus 10_{2} equals 01_{2}.Q13.What type of logic gates are added to a parallel adder to enable it to subtract?Q14.How many of these gates would be needed to add a four-digit number?Q15.In the add mode, what does the output of C_{2} indicate?Q16.In the subtract mode, a 1 at C_{0} performs what portion of the R’s complement?Q17.In the subtract mode, which portion of the problem is complemented? FLIP-FLOPSFlip-flops (FFs) are devices used in the digital field for a variety of purposes. When properlyconnected, flip-flops may be used to store data temporarily, to multiply or divide, to count operations, orto receive and transfer information.Flip-flops are bistable multivibrators. The types used in digital equipment are identified by theinputs. They may have from two up to five inputs depending on the type. They are all common in onerespect. They have two, and only two, distinct output states. The outputs are normally labeled Q and Qand should always be complementary. When Q = 1, then Q = 0 and vice versa.In this section we will discuss four types of FFs that are common to digital equipment. They are theR-S, D, T, and J-K FFs.R-S FLIP-FLOPThe R-S FF is used to temporarily hold or store information until it is needed. A single R-S FF willstore one binary digit, either a 1 or a 0. Storing a four-digit binary number would require four R-S FFs.The standard symbol for the R-S FF is shown in figure 3-12, view A. The name is derived from theinputs, R for reset and S for set. It is often referred to as an R-S LATCH. The outputs Q and Q arecomplements, as mentioned earlier.

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