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Fundamentals of Digital Electronics - Lab 3

Binary Addition Trước khi tiến hành phòng thí nghiệm này, nó là hữu ích để xem xét một số chi tiết bổ sung nhị phân. Cũng như trong Ngoài ra số thập phân, thêm từ 0 đến giá trị bất kỳ để lại con số không thay đổi: 0 + 0 = 0, trong khi 1 + 0 = 1. Tuy nhiên, khi bạn thêm 1 + 1 ngoài nhị phân, kết quả không phải là "2" (một biểu tượng không tồn tại trong hệ thống số nhị phân), nhưng "10", "1" trong "đặt hàng hai" và một. | Lab 3 Binary Addition Before proceeding with this lab it is helpful to review some details of binary addition. Just as in decimal addition adding 0 to any value leaves that number unchanged 0 0 0 while 1 0 1. However when you add 1 1 in binary addition the result is not 2 a symbol which does not exist in the binary number system but 10 a 1 in the twos place and a zero in the ones place. If you write this addition vertically you would recite One and one are two write down the zero carry the one 1 1 10 Figure 3-1. Single-Bit Addition Below is the truth table for single-bit addition. There are two input columns one for each addend A1 and A2 and two output columns one for the ones-place sum and one for the carried bit Table 3-1. Truth Table for Addition A1 A2 Sum with Carry 0 0 0 0 0 1 1 0 1 0 1 0 1 1 0 1 National Instruments Corporation 3-1 Fundamentals of Digital Electronics Lab 3 Binary Addition Which of the fundamental gates can you use to implement the output columns Note that A1 XOR A2 reproduces the Sum output and A1 AND A2 the Carry output so a LabVIEW implementation of this 1-bit addition truth table is Figure 3-2. Half Adder Built from XOR and AND Gates This digital building block is called a half adder. The term half adder refers to the fact that while this configuration can generate a signal to indicate a carry to the next highest order bit it cannot accept a carry from a lower-order adder. A full adder has three inputs. In addition to the two addends there is also a carry in input which adds the bit carried from the previous column as in the middle column in the following example 101 101 1010 Figure 3-3. Three-Bit Binary Addition The truth table for a single-bit full adder therefore has three inputs and thus eight possible states Table 3-2. Truth Table for Addition with a Carry In Carry In A1 A2 Sum Carry Out 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 1 0 1 1 0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 1 1 1 1 Fundamentals of Digital Electronics 3-2 National Instruments .