How to start this truth table from function

Question

I understand truth tables and do them fine when it's Z = A + B + ABC' etc. but how do I start a truth table where I'm suppose to take the function Y = 2X + 3 and construct a truth table from that? X is the input 3 bit(x1x2x3) and Y is the output with 5 bit(y1y2y3y4y5). I am clueless on how to start and just need help pointing me in the right direction.

Answer 1

Hints (without full solution)

1. Enumerate the binary inputs
2. Complete the Y column in decimal
3. Convert Y to binary
4. Drop the decimal columns

Full solution (don't peek)

(1) Enumerate the binary inputs:

X x3 x2 x1
----------
0  0  0  0
1  0  0  1
2  0  1  0
3  0  1  1
4  1  0  0
5  1  0  1
6  1  1  0
7  1  1  1

(2) Complete the Y column in decimal:

X x3 x2 x1  |  Y
----------------
0  0  0  0  |  3
1  0  0  1  |  5
2  0  1  0  |  7
3  0  1  1  |  9
4  1  0  0  | 11
5  1  0  1  | 13
6  1  1  0  | 15
7  1  1  1  | 17

(3) Convert Y to binary:

X x3 x2 x1  |  Y  y5 y4 y3 y2 y1
--------------------------------
0  0  0  0  |  3   0  0  0  1  1
1  0  0  1  |  5   0  0  1  0  1
2  0  1  0  |  7   0  0  1  1  1
3  0  1  1  |  9   0  1  0  0  1
4  1  0  0  | 11   0  1  0  1  1
5  1  0  1  | 13   0  1  1  0  1
6  1  1  0  | 15   0  1  1  1  1
7  1  1  1  | 17   1  0  0  0  1

(4) Drop the decimal columns:

x3 x2 x1  |  y5 y4 y3 y2 y1
---------------------------
 0  0  0  |   0  0  0  1  1
 0  0  1  |   0  0  1  0  1
 0  1  0  |   0  0  1  1  1
 0  1  1  |   0  1  0  0  1
 1  0  0  |   0  1  0  1  1
 1  0  1  |   0  1  1  0  1
 1  1  0  |   0  1  1  1  1
 1  1  1  |   1  0  0  0  1