A 7-segment display is a component used to display a digit on devices such as calculators. A 7-segment display consists of seven lights (called segments) which can be illuminated individually to make the shapes of digits. For example, the digit 3 could be displayed by illuminating five of the seven segments like this (black shading indicates an illuminated segment):
Figure 7 shows part of a logic circuit which is designed to take a binary representation of a single decimal digit as its input and light up the segments to display the decimal digit. The part of the circuit shown controls the lighting of just one segment of the display.
The inputs to the circuit are X3, X2, X1 and X0. Together these form the binary representation of the decimal digit to display. For example, if the inputs to the circuit were:
then the display would need to show this pattern:
as 0101 is the binary representation of the decimal digit 5
The output Q is connected to one segment of the display. When Q is 1 this segment lights up, when it is 0 the segment does not light up.
Complete every empty cell in the truth table below for the circuit in Figure 7
• The listed inputs to the table (X3, X2, X1, X0) represent the decimal digits 0–9 in binary, which are the only allowed inputs.
• The letters A–E have been used to label intermediate points on the circuit in Figure 7 to help you to work out the final output Q
• Some of the cells have been completed for you.