The parallel binary adder of figure 641 has limited

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Unformatted text preview: ch column above the first. To illustrate how the adder of Figure 6.41 works, let us see how it will add two numbers say, 9 and 11. The binary equivalent of decimal 9 is 1001, and that of decimal 11 is 1011. Figure 6.42 shows the binary adder with these inputs. As shown in the figure, the half-adder adds 1 + 1 to give a sum of 0 and a carry 1. The carry goes into the first full-adder, which adds 0 + 1 + 1 to get a sum of 0 and a carry of 1. This carry goes into the next full-adder, which adds 0 + 0 + 1 to get a sum of 1 and a carry of 0. The last full-adder adds 1 + 1 + 0 to get a sum of 0 and a carry of 1. The final output of the system is 10100. The decimal equivalent of binary 10100 is 20 which is the correct decimal sum of 9 and 11. The parallel binary adder of Figure 6.41 has limited capacity. The largest binary numbers that can be added using it are 1111 and 1111. Hence its maximum capacity is: 15 +15 30 1111 + 1111 11110 In order to increase the capacity, more full-adders can be connected to the left end of the system. For instance, to add six bit numbers, two more full-adders must be connected and for adding eight bit numbers, four more full-adders must be connected to the left end of the full-adder of Figure 6.41. Points to Remember 1. Boolean algebra deals with the binary number system. That is, the variables used in the Boolean equations may have only two possible values (0 and 1). 2. In Boolean algebra, the 'OR' operator used for logical addition is represented by the symbol '+'; the 'AND' operator used for logical multiplication is represented by the symbol ' • '; and the 'NOT' operator used for complementation is represented by the symbol'-'. 3. As regards precedence of Boolean operators, 'NOT' operator takes precedence over 'AND' and 'OR' operators, and 'AND' operator takes precedence over 'OR' operator. 4. The postulates of Boolean algebra are (a) A = 0 if and only if A is not equal to 1 (b) A = 1 if and only if A is not equal to 0 (c) x + 0 = x (d) x • 1 = x (e) x + y = y...
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