This question is incomplete, the complete question is;
Your boss asks you to design a Boolean circuit that verifies whether a given integer 0 < x < 16 is divisible by 5.
Every such number is represented in binary using four bits, say b₃b₂b₁b₀, and so your Boolean circuit will have four inputs. For instance, the number 13 is written in binary as 1101 and so to test its divisibility by 5 a user would feed the values b₀ = 1, b₁ = 0, b₂ = 1, and b₃ = 1 into the inputs of your circuit.
The Boolean circuit will have a single output, which should deliver the value 1 if the iput values represent a number that is divisible by 5 and 0 otherwise.
a) write down the truth table of the Boolean function F(b₀,b₁,b₂b₃) that implements this "divisible by 5" operation
b) construct a Boolean expression in disjunctive normal form that implements the Boolean function yo wrote down in a)
Answer:
Given that;
integer range = 0≤ x ≤ 16
within 4bits, we can represnt each number
(0,5,10,15)
a)
Truth table for function that implements divisible by 5
Integer B3 B2 B1 B0 Y
0 0 0 0 0 1
1 0 0 0 1 0
2 0 0 1 0 0
3 0 0 1 1 0
4 0 1 0 0 0
5 0 1 0 1 1
6 0 1 1 0 0
7 0 1 1 1 0
8 1 0 0 0 0
9 1 0 0 1 0
10 1 0 1 0 1
11 1 0 1 1 0
12 1 1 0 0 0
13 1 1 0 1 0
14 1 1 1 0 0
15 1 1 1 1 1
b)
Boolean expression that implements the Boolean function from a)
from the truth table;
Boolean expression Y is;
Y = b⁻₃b⁻₂b⁻₁b⁻₀ / y₁ + b⁻₃b₂b⁻₁b₀ / y₂ + b₃b⁻₂b₁b⁻₀ / y₃ + b₃b₂b₁b₀ / y₄