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# What is a parallel adder?

The adders discussed in the previous section have been limited to adding single-digit binary numbers and carries. The largest sum that can be obtained using a full adder is 11… 2 . Parallel adders let us add multiple-digit numbers. If we place full adders in parallel, we can add two- or four-digit numbers or any other size desired. Figure 3-9 uses STANDARD SYMBOLS to show a parallel adder capable of adding two, two-digit 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 3-9. -Parallel binary adder. Now let's add some two-digit 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 3-10. Adder 1 produces a sum (S 1 ) of 0 and a carry (C 1 ) of 1. Adder 2 gives us a sum (S 2 ) (MORE)