# COMP2421 Assignment 5

MA Mingyu (Derek) | 14110562D | Nov 12, 2017
derek.ma | derek.ma@connect.polyu.hk

## Question 1

Characteristic table:

$$S$$ $$R$$ $$Q(t)$$ $$Q(t+\Delta)$$
0 0 0 disallowed
0 0 1 disallowed
0 1 0 1
0 1 1 1
1 0 0 0
1 0 1 0
1 1 0 0
1 1 1 1

K-map:

row:$$SR$$; col:$$Q(t)$$ 00 01 11 10
0 X 1 0 0
1 X 1 1 0

Next-state equation:

$$Q(t+\Delta) = \overline{S(t)} + R(t)Q(t)$$

The relationship between this latch and the one using NOR gates is exact opposite.

$$S$$ here is actually $$\overline{S}$$, and $$R$$ here is actually $$\overline{R}$$ compared to the one using NOR gates.

## Question 3

Characteristic table for this latch:

$$E$$ $$D$$ $$Q$$ $$Q_{next}$$ $$\overline{Q_{next}}$$
0 X 0 0 1
0 X 1 1 0
1 0 X 0 1
1 1 X 1 0

where X means "don't care the value of this variable".

Another possible characteristic table is:

$$E$$ $$D$$ $$Q$$ $$Q_{next}$$ $$\overline{Q_{next}}$$
0 0 X $$Q$$ $$\overline{Q}$$
0 1 X $$Q$$ $$\overline{Q}$$
1 0 X 0 1
1 1 X 1 0