3-8When A, B, and the carry-in are all HIGH, a sum of 1 and a carry-out are produced. First, consider Aand B. When both are HIGH, the output of gate 1 is LOW, and the output of gate 2 is HIGH, giving us acarry-out at gate 5. The carry-in produces a 1 output at gate 3, giving us a sum of 1. The output of the fulladder is 11_{2}. The sum of 1_{2} plus 1_{2} plus 1_{2} is 11_{2}.PARALLEL ADDERSThe adders discussed in the previous section have been limited to adding single-digit binary numbersand 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-digitbinary 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 symbolmay actually contain many and various types of gates and circuits. The addend would be input on the Ainputs (A_{2} = MSD, A_{1} = LSD), and the augend input on the B inputs (B_{2} = MSD, B_{1} = LSD). For thisexplanation 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 arenumbers at the appropriate inputs. The addend inputs will be 1 on A_{2} and 0 on A_{1}. The augend inputs willbe 0 on B_{2} and 1 on B_{1}. Working from right to left, as we do in normal addition, let’s calculate the outputsof 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} is1 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 theoutputs (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}, asshown 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})

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