Q.12 What is the output of C₁?

SUBTRACTION

Subtraction is accomplished in computers by the R's complement and add method. This is the same method you used in chapter 1 to subtract binary numbers.

R's complement subtraction allows us to use fewer circuits than would be required for separate add and subtract functions. Adding X-OR gates to full adders, as shown in figure 3-11, enables the circuit to perform R's complement subtraction as well as addition.

Figure 3-11. - R's complement adder/subtracter.

To add two numbers using this circuit, the addend and augend are applied to the A and B inputs. The B inputs are applied to one input of the X-OR gates. A control signal is applied to the other input of the X-OR gates. When the control signal is LOW, the circuit will add; and when it is HIGH, the circuit will subtract.

In the add mode, the outputs of the X-OR gates will be the same as the B inputs. Addition takes place in the same manner as described in parallel addition.

Before we attempt to show subtraction, let's review R's complement subtraction. To subtract 10₂ from 11₂, write down the minuend (11₂). Perform the R's complement on the subtrahend. Now add the minuend and the complemented subtrahend.

Disregard the most significant 1, and the difference between 11₂ and 10₂ is 01₂. The most significant 1 will not be used in the example shown in the following paragraph.

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.

Q.13 What type of logic gates are added to a parallel adder to enable it to subtract?
Q.14 How many of these gates would be needed to add a four-digit number?
Q.15 In the add mode, what does the output of C₂ indicate?
Q.16 In the subtract mode, a 1 at C ₀ performs what portion of the R's complement?
Q.17 In the subtract mode, which portion of the problem is complemented?