Question

Design a combinational circuit which inputs a three-bit binary number, and outputs the input number PLUS two if the input is less then or equal to 3, and outputs the minus two if the input is greater than 3. This should include the truth table for the operation, the karnaugh map(s), and the resulting circuit.

Answer 1

In the question it is given that input is a 3-bit binasy. number that means it must be a number in between 1000 to 111) sie bet o to 7 (if we consider it's decimal Equivalent) → And out out a s input +2 (if input 43) input-2 (if input 73) That means if we consider it's decimal equivalent, then Input output Input output com J 4 6 3 4 5. 3 7 y we have seen that the maximum decimal equivalent of output is 5. which is less than 7lie 11). so in output side we have to consider 3 bit binary number. Truth Table All possible Decimal Decimal combination Equivalent Equivalent out put of In put of Input of output MSB LSB MSB LSB x y z ...... .. . ... A B C O O O...-..-.O. -.---.2 -..........-0 0 0 0 1 ------ --- --- 3...... 0 0 1 0 ---------2--------- 4 -------- 1 0 0 0 1 1 .......3.. - -- 5 --- --- 0 1 1 0 0 .......4-------2----- O o 1 0 1 ---5----------3----~ 0 1 1 1 O ... - 6 -- -- -- .4 ....-1 0 0 1 1 1 ... ..7........-5 .--- -1 0 1 م ن ى To get the desired result of output, we have to take (consider) each bits of output separately. 7 FOR A we have to take the K-map of variable x,y,z where And e A= 1, for x, y, z 7 010,011, 110, 11

A That means, A= f(x, 9, 2) = {(2, 3, 6, 7) Zoo old FOR "B" Similary B = f(x,12)= = (0,1,4,5) 92 no a u a to similarly C = f (M. y, z) = {(1, 3, 5,7) Similare e TC =Z Z M X. o Isa (opez (input) (output)