A seven-segment display is a device composed of 7 elements, as shown in the figure below. Each element is selectively lit to form patterns such as numbers or letters. For example, to display '0', the segments A, B, C, D, E and F have to be simultaneously lit. A circuit decoder takes in a 4-bit binary number and produces the outputs A, B, C, D, E, F and G. The outputs of the decoder are then fed to the seven-segment display as shown in the figure. The seven-segment display should show the sum of the 4-bit input + 1. For example, if the 4-bit input is 000 , the decoder’s output will lit up the seven-segment display that will show the numerical number 1. This corresponds to the decoder output of 01100002. In the case wherein the 4-bit input = 1001 , the decoder’s output will lit up the seven-segment display that will show the numerical number 0. This corresponds to the decoder output of 1111110 . The decoder’s output line should be logic “1” if the segment will be lit and “0” otherwise. Assume that the input values will be limited to values 0000 up to 1001 . 1. Write the truth table of the described circuit decoder. Use W,X,Y,Z as input variables and A, B, C, D, E, F, G as output variables. 2. Formulate the simplest SOP expression of output variables B, D and F using K-map. Draw the circuits of the formulated SOPexpressions.
A seven-segment display is a device composed of 7 elements, as shown in the figure below. Each element is selectively lit to form patterns such as numbers or letters. For example, to display '0', the segments A, B, C, D, E and F have to be simultaneously lit.
A circuit decoder takes in a 4-bit binary number and produces the outputs A, B, C, D, E, F and G. The outputs of the decoder are then fed to the seven-segment display as shown in the figure. The seven-segment display should show the sum of the 4-bit input + 1. For example, if the 4-bit input is 000 , the decoder’s output will lit up the seven-segment display that will show the numerical number 1. This corresponds to the decoder output of 01100002. In the case wherein the 4-bit input = 1001 , the decoder’s output will lit up the seven-segment display that will show the numerical number 0. This corresponds to the decoder output of 1111110 . The decoder’s output line should be logic “1” if the segment will be lit and “0” otherwise. Assume that the input values will be limited to values 0000 up to 1001
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1. Write the truth table of the described circuit decoder. Use W,X,Y,Z as input variables and
A, B, C, D, E, F, G as output variables.
2. Formulate the simplest SOP expression of output variables B, D and F using K-map. Draw the circuits of the formulated SOPexpressions.
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