SOP and Traffic Light Circuit Design using Logic Gates

Task 1
SOP;
F(A,B,C,D) = ΣM (4,8,9,12,13,14)
=A’B’C’D’+AB’C’D’+AB’C’D+AB’C’D+ABC’D+ABCD’
=A’B’C’D’+A (B’C’D’+B’C’D) +AB (C’D’+C’D+CD’)
=A’B’C’D’+A (B’C’ (D’+D)) +AB (C’ (D’+D) +CD’))
=A’B’C’D’+AC’ (B’+B) +ABCD
=AC’+B
This circuit below satisfies the equation
The circuit can be redesigned using NAND gates as below

Task 2:
1. Block diagram for the traffic sequence
2. Truth table for outputs
3. Boolean expressions for each light

We can derive outputs of each lamp:
Red= ABC’D’
Amber= A’BC’D
Green = A’B’CD’
4. Using K-Maps to minimize each expression
This gives output as:
RED = A
AMBER= A’.B
GREEN=A’.B’
HALT= A’.B’= WALK
5. Use AND, OR and NOT GATES to show outputs: