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The vast applications of ex-OR logic include in giving a "I" output when the binary input string is of odd parity (has odd number of l"s) and also can be employed as controlled inverters (NOT logic) on a 2-in-l adder/subtractor circuit for sequential machines as shown in Fig. 19. The cirCUitry required to perform arithmetic using decimal operands (BCD) is more complex than that needed for binary arithmetic. A uniform method of propagating carries between adjacent positions is not possible since the weights Wi and Wi+ 1 of adjacent bits do not differ by constant factor.
Fig. 25 shows the excitation tables for clifferent types of flipflops. A sequential circuit is an interconnection of flipflops and gates. This necessarily includes primary output points and inputs. Given a finite state machine with clearly defined states, it is possible to design and constmct the circuit using several types of flipflops to meet the implementation constraints. This process is called circuit synthesis. A state diagram is an alternative approach for stating sequential circuits. SR = 00 or 10 10 SR = 00, 01 01 Fig.
I. I chart is shown on next page. 34 Computer architecture and systems design Table To TableT! minterms A B C 0 0 1 2 8 5 9 10 7 13 15 0 0 0 1 0 1 1 0 1 1 --~~~ 0 0 0 0 1 0 0 1 1 A B C 0 0 0 1 0 0 0 1 1 0 1 0 0 1 1 0 1 1 1 1 1 0, 1 0,2 0,8 1,5 1,9 2, 10 8,9 8,10 5, 7 5, 13 9, 13 7,15 13, 15 ° 0 0 o - 0 1 1 0 0 0 0 1 °°- ° - 1 - 1 0 0 0 0 0 1 1 1 1 0 1 1 0 o - 0 0 1 - 0 1 1 1 1 1 TableT2 A B C 0 The terms labelled PI, P2, P3 and P4 in Table T2 cannot be further combined and therefore form the set of prime implicants of the given function.