Design a Binary-Coded Hexadecimal decoder (logic circuit) for the Hexa digits A through F,

abdullah7saman wrote:

Design a Binary-Coded Hexadecimal decoder (logic circuit) for the Hexa digits A through F, assuming that the digits O through 9 are of no interest anymore (don't care case). Assume that the inputs are in the range 1010 to 1111, and that the output characters appear in the seven-segment display in the following way: ABCDEF

To design a binary-coded hexadecimal (BCD) decoder for the hex digits A through F, we first need to identify the input and output conditions for each segment of the seven-segment display. I'll list the input conditions (A-F in binary) along with the corresponding output segments that should be active:

A (1010) -> ABCDEFG (output segments)
B (1011) -> ABGCDEF (output segments)
C (1100) -> AFGED (output segments)
D (1101) -> ABEDCF (output segments)
E (1110) -> AFGEC (output segments)
F (1111) -> AFGE (output segments)

Now, let's create the logic equations for each output segment based on the input conditions:

A = A3'A2A1'A0 + A3A2A1'A0
B = A3'A2A1'A0 + A3A2A1'A0'
C = A3'A2A1A0 + A3A2A1'A0'
D = A3'A2A1A0 + A3A2A1'A0 + A3A2A1A0'
E = A3'A2A1'A0 + A3A2A1A0 + A3A2A1A0'
F = A3'A2A1'A0 + A3A2A1A0 + A3A2A1A0'
G = A3'A2A1A0 + A3A2A1A0'

Where A3, A2, A1, and A0 are the BCD input bits, and A, B, C, D, E, F, G are the output segments of the seven-segment display.

You can now design the logic circuit for the binary-coded hexadecimal decoder using AND, OR, and NOT gates based on these equations.