Hi
I'm supposed to design a 2 bit binary counter with an extra input, x, to decide whether it should count up or down (x=1 counts up). The design uses two D-flip-flops.
To help I got a couple of truth tables to fill in. The first is for both flip-flops, D1 and D2. Then this one is split to two separate tables, for each flip-flop.
q1 is the output of the D1 flip-flop and so forth.
This is how I filled the tables:

q1q2|x=0|x=1
____|___|___
00  | 11|01
____|___|___
01  | 00|10
____|___|___
11  | 10|00
____|___|___
10  | 01|11
____|___|___

     D1 D2

q1q2|x=0|x=1
____|___|___
00  |  1|  1
____|___|___
01  |  0| 0
____|___|___
11  |  0| 0
____|___|___
10  |  1| 1
____|___|___

     D1

q1q2|x=0|x=1
____|___|___
00  | 1 |0
____|___|___
01  | 0 |1
____|___|___
11  | 1 |0
____|___|___
10  | 0 |1
____|___|___

     D2

When I collect the ones to make the boolean functions, I get:

D1 = q1' + q2'
D2 = x'q1'q2' + xq1'q2 + x'q1q2 + xq1q2'

But D2 equals 1, so I must have made an error somewhere. Please help.

 

How does D2 equal 1? It looks correct to me. Your equation for D1 is off, however.

 

How does D2 equal 1?

Because I suck at Boolean algebra..
The correct answer should be:
D1 = q2'
D2 = (x(XOR)q1(XOR)q2)'
but I also separated the tables wrong, so D1=D2, and vice versa.