Mercenary Motors has expanded into the calculator business. You need to design t

Question

Mercenary Motors has expanded into the calculator business. You need to design the eke cuitry for the display readout on a new calculator. This design involves a two-step process. a. Any digit 0, 1, 9 put into the calculator is first converted to binary form. Part (a) of the accompanying figure illustrates this conversion, which involves four separate networks, one each for xi to x4. Each network has 10 inputs, but only 1 input can be on at any given moment. Write a Boolean expression and then draw a network for

b. The binary form of the digit is then converted into a visual display by activating a - pattern of seven outputs arranged as shown in figure (b). To display the digit 3. for example, yll y 2, y3, y5, and y7 must be on, as in figure (c)%u2022 Thus, the second step of the process can be represented by figure (d), which involves seven separate networks one each for yl to y7, each with four inputs, x1 to x4. Write a truth function, a Boolean expression, and a network for y5 and for y6.

Explanation / Answer

I will write the expressions, drawing them is pretty easy.

Let me denote the numbers as a0, a1, .. a9

So now we have

x4 = a9 + a8 -- + is or and . is and

x3 = a4 + a5 + a6 +a7

x2 = a2 + a3 + a6 + a7 + a9

x1 = a1 + a3 + a5 + a7 + a9

the other part is more difficult, if you want the shortest expressions then you require k-maps

but for normal ones we can directly write them

y5 is true for - 0,1,2,3,4,7,8,9 -- not true only for 5,6

So y5 = ~(~x4.x3.x2.~x1 + ~x4.x3.x2.~x1)

y6: is high for 0, 2,6,8 -- all evens except 4

y6 = (~x1). ~(~x4.x3.~x2.~x1)

comment if you have any doubt

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