onsider a special purpose decoder that is called BCD to seven-segment decoder. The decoder takes a 4-bit Binary Coded Decimal (BCD) number X3 X2 X4 X0 (0-9) and produces 7 outputs a, b, c, d, e, f, and g The specification of this circuit is as follows: ⚫ The 7 outputs of the decoder are connected to LED segments as shown in the figure below. The LEDs are active low, ie, the LED emits light when it is connected to logic 0. • The decoder output is determined in a way so that the LED segments display the decimal representation of the input. For example, if the input X3 X2 X1 X0 is 0001 respectively (which is equivalent to decimal 1), the outputs a, b, c, d, e, f, and gare 1001111 showing the letter 1 on the display (remember the LEDs are active low). Decoder W- 4x7 e U Answer the following questions: a. Fill in the truth table of that decoder. Choose a good value for the output when the input is greater than decimal 9. b. Derive the simplified Boolean expressions for the outputs a, b, c, d, e, t and g using K-maps. Decimal Corresponding Digit LED segments Input X2 0 X2 Xo Output def & X3 0 0 0 abc 0 0 0 0 0 1 0 2 14 1 1 1 1 1 15
Consider a special purpose decoder that is called BCD to seven-segment decoder. The decoder takes a 4-bit Binary Coded Decimal (BCD) number X3 X2 X4 X0 (0-9) and produces 7 outputs a, b, c, d, e, f, and g The specification of this circuit is as follows:
⚫ The 7 outputs of the decoder are connected to LED segments as shown in the figure below. The LEDs are active low, ie, the LED emits light when it is connected to logic 0.
• The decoder output is determined in a way so that the LED segments display the decimal representation of the input. For example, if the input X3 X2 X1 X0 is 0001 respectively (which is equivalent to decimal 1), the outputs a, b, c, d, e, f, and gare 1001111 showing the letter 1 on the display (remember the LEDs are active low).
Decoder
W-
4x7
e
U
Answer the following questions:
a. Fill in the truth table of that decoder. Choose a good value for the output when the input is greater than decimal 9. b. Derive the simplified Boolean expressions for the outputs a, b, c, d, e, t and g using K-maps.
Decimal
Corresponding
Digit
LED segments
Input
X2
0
X2
Xo
Output
def
&
X3
0
0
0
abc
0
0 0
0
0
1
0
2
14
1
1
1
1
1
15
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