38
When A, B, and the carryin are all HIGH, a sum of 1 and a carryout are produced. First, consider A
and B. When both are HIGH, the output of gate 1 is LOW, and the output of gate 2 is HIGH, giving us a
carryout at gate 5. The carryin produces a 1 output at gate 3, giving us a sum of 1. The output of the full
adder is 11_{2}. The sum of 1_{2} plus 1_{2} plus 1_{2} is 11_{2}.
PARALLEL ADDERS
The adders discussed in the previous section have been limited to adding singledigit binary numbers
and carries. The largest sum that can be obtained using a full adder is 11_{2}.
Parallel adders let us add multipledigit numbers. If we place full adders in parallel, we can add two
or fourdigit numbers or any other size desired.
Figure 39 uses STANDARD SYMBOLS to show a parallel adder capable of adding two, twodigit
binary numbers. In previous discussions we have depicted circuits with individual logic gates shown.
Standard symbols (blocks) allow us to analyze circuits with inputs and outputs only. One standard symbol
may actually contain many and various types of gates and circuits. The addend would be input on the A
inputs (A_{2} = MSD, A_{1} = LSD), and the augend input on the B inputs (B_{2} = MSD, B_{1} = LSD). For this
explanation we will assume there is no input to C_{0} (carry from a previous circuit).
Figure 39. —Parallel binary adder.
Now let’s add some twodigit numbers. To add 10_{2} (addend) and 01_{2} (augend), assume there are
numbers at the appropriate inputs. The addend inputs will be 1 on A_{2} and 0 on A_{1}. The augend inputs will
be 0 on B_{2} and 1 on B_{1}. Working from right to left, as we do in normal addition, let’s calculate the outputs
of each full adder.
With A_{1} at 0 and B_{1} at 1, the output of adder 1 will be a sum (S_{1}) of 1 with no carry (C_{1}). Since A_{2} is
1 and B_{2} is 0, we have a sum (S_{2}) of 1 with no carry (C_{2}) from adder 1. To determine the sum, read the
outputs (C_{2}, S
_{2}, and S_{1}) from left to right. In this case, C_{2} = 0, S_{2} = 1, and S_{1} = 1. The sum, then, of 10_{2}
and 01_{2} is 011_{2} or 11_{2}.
To add 11_{2} and 01_{2}, assume one number is applied to A_{1} and A_{2}, and the other to B_{1} and B_{2}, as
shown in figure 310. Adder 1 produces a sum (S_{1}) of 0 and a carry (C_{1}) of 1. Adder 2 gives us a sum (S_{2})

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