3-11
Now let’s subtract 102 from 112 using the adder/subtracter circuit. The minuend (112) is input on the
A terminals, and the subtrahend (102) is input on the B terminals. In the subtract mode, a 1 from the
control circuit is input to each of the X-OR gates and to the C0 carry input. By applying a 1 to each of the
X-OR gates, you find the output will be the complement of the subtrahend input at B1 and B2. Since B1 is
a 0, the output of X-OR 1 will be 1. The input B2 to X-OR 2 will be inverted to a 0. The HIGH input to C0
acts as a carry from a previous circuit. The combination of the X-OR gates and the HIGH at C0 produces
the R’s complement of the subtrahend. The full adders add the minuend and the R’s complement of the
subtrahend and produce the difference. The output of C2 is not used. The outputs of S2 and S1 are 0 and 1,
respectively, indicating a difference of 012. Therefore, 112 minus 102 equals 012.
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 C2 indicate?
Q16. In the subtract mode, a 1 at C0 performs what portion of the R’s complement?
Q17. In the subtract mode, which portion of the problem is complemented?
FLIP-FLOPS
Flip-flops (FFs) are devices used in the digital field for a variety of purposes. When properly
connected, flip-flops may be used to store data temporarily, to multiply or divide, to count operations, or
to receive and transfer information.
Flip-flops are bistable multivibrators. The types used in digital equipment are identified by the
inputs. They may have from two up to five inputs depending on the type. They are all common in one
respect. They have two, and only two, distinct output states. The outputs are normally labeled Q and Q
and 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 the
R-S, D, T, and J-K FFs.
R-S FLIP-FLOP
The R-S FF is used to temporarily hold or store information until it is needed. A single R-S FF will
store 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 the
inputs, R for reset and S for set. It is often referred to as an R-S LATCH. The outputs Q and Q are
complements, as mentioned earlier.
