An electronic game uses an array of seven LEDs (light-emitting diodes) to display the results of a random roll of a die. A decoder is to be designed to illuminate the appropriate diodes for the display of each of the six die values. The desired display patterns are shown in Figure 3-57.

Figure 3-57

(a) Use a 3–to–8-line decoder and OR gates to map the 3-bit combinations on inputs X₂, X₁, and X0 for values 1 through 6 to the outputs a through g. Input combinations 000 and 111 are don’t-cares.

(b) Note that for the six die sides, only certain combinations of dots occur.
For example, dot pattern A = 5d 6 and dot pattern B = 5a, g 6 can be used for representing input values 1, 2, and 3 as {A}, {B}, and {A, B}.
Deine four dot patterns A, B, C, and D, sets of which can provide all six output patterns. Design a minimized custom decoder that has inputs X₂, X₁, and X₀ and outputs A, B, C, and D, and compare its gate-input cost to that of the 3-to-8 decoder and OR gates in part (a).

Transcribed Image Text:

b cde 10E 1 2 4 5 9