1. A digital circuit has 4 inputs D, C, B, A representing the binary values 0000 to 1111 (0 to 15 decimal). The output F is true if the input falls in the range 8 to 10 (inclusive), or if the input is divisible by 3, or if the input is divisible by 7. It is false otherwise. Zero is considered as indivisible by 3 or 7. (10 marks) LO 01 a) Construct a truth table for this system b) From the truth table write down a Boolean equation for F in terms of D, C, B, A c) Using either Boolean algebra or Karnaugh maps, obtain a simplified expression for F. d) Draw a circuit to implement the circuit for F.

1. A digital circuit has 4 inputs D, C, B, A representing the binary values 0000 to 1111 (0 to 15 decimal). The output F is true if the input falls in the range 8 to 10 (inclusive), or if the input is divisible by 3, or if the input is divisible by 7. It is false otherwise. Zero is considered as indivisible by 3 or 7. (10 marks) LO 01 a) Construct a truth table for this system b) From the truth table write down a Boolean equation for F in terms of D, C, B, A c) Using either Boolean algebra or Karnaugh maps, obtain a simplified expression for F. d) Draw a circuit to implement the circuit for F