---
tags:
  - sorbonne
  - in0ormatique
  - architecture-des-ordinateurs
  - td
semestre: 3
---
TME sont encore moins bons que les partiels
|> rendu semaine prochaine

---

| $a$ | $b$ | $c$ | $\bar b.a.c$ | $s$ |
| --- | --- | --- | ------------ | --- |
| 1   | 1   | 1   | 0            | 1   |
| 1   | 1   | 0   | 0            | 1   |
| 1   | 0   | 1   | 1            | 1   |
| 1   | 0   | 0   | 0            | 0   |
| 0   | 1   | 1   | 0            | 1   |
| 0   | 1   | 0   | 0            | 1   |
| 0   | 0   | 1   | 0            | 0   |
| 0   | 0   | 0   | 0            | 0   |
$b+\bar b.a.c = (b+\bar b).(b+a.c) = b+a.c$

$(\bar a.\bar b.\bar c)+(\bar a.b.\bar c)+(\bar a.b.c)+(a.b.c)$

| $a$ | $b$ | $c$ | $b+a.c$ | $(a+b).(a+c)$ |
| --- | --- | --- | ------- | ------------- |
| 0   | 0   | 0   | 0       | 0             |
| 0   | 0   | 1   | 0       | 0             |
| 0   | 1   | 0   | 0       | 0             |
| 0   | 1   | 1   | 1       | 1             |
| 1   | 0   | 0   | 0       | 1             |
| 1   | 0   | 1   | 1       | 1             |
| 1   | 1   | 0   | 1       | 1             |
| 1   | 1   | 1   | 1       | 1             |

| $a$ | $b$ | $\mathrm{xor}(a,b)$ |
| --- | --- | ------------------- |
| 0   | 0   | 0                   |
| 0   | 1   | 1                   |
| 1   | 0   | 1                   |
| 1   | 1   | 0                   |
$(\bar a.b)+(a.\bar b)$

$\mathrm{mux2}(a,b,c) = a.\bar c+b.c$

| $a$ | $b$ | $c$ | $\mathrm{mux2}(a,b,c)$ |
| --- | --- | --- | ---------------------- |
| 0   | 0   | 0   | 0                      |
| 0   | 0   | 1   | 0                      |
| 0   | 1   | 0   | 0                      |
| 0   | 1   | 1   | 1                      |
| 1   | 0   | 0   | 1                      |
| 1   | 0   | 1   | 0                      |
| 1   | 1   | 0   | 1                      |
| 1   | 1   | 1   | 1                      |
$(\bar a.b.c)+(a.\bar b.\bar c)+(a.b.\bar c)+(a.b.c)$

3 entrées ($u_1$ et $u_2$, $c_{in}$)
2 sorties ($s$, $c_{out}$)

| $u_1$ | $u_2$ | $c_{in}$ | $s$ | $c_{out}$ |
| ----- | ----- | -------- | --- | --------- |
| 0     | 0     | 0        | 0   | 0         |
| 0     | 0     | 1        | 1   | 0         |
| 0     | 1     | 0        | 1   | 0         |
| 0     | 1     | 1        | 0   | 1         |
| 1     | 0     | 0        | 1   | 0         |
| 1     | 0     | 1        | 0   | 1         |
| 1     | 1     | 1        | 1   | 1         |
| 1     | 1     | 0        | 0   | 1         |
$s=(\bar u_1.\bar u_2.c_{in})+(\bar u_1.u_2.\bar c_{in})+(u_1.\bar u_2.\bar c_{in})+(u_1.u_2.c_{in})=u_1\oplus u_2\oplus c_{in}$ où $\oplus$ est $\mathrm{xor}$ (à refaire)
$c_{out}=(\bar u_1.u_2.c_{in})+(u_1.\bar u_2.c_{in})+(u_1.u_2.c_{in})+(u_1.u_2.\bar c_{in})=a.b+a.c_{in}+b.c_{in}=c_{in}.(a\oplus b)+a.b$ (à refaire)

$s = (\bar a . \bar b . c)+(\bar a.b.\bar c)+(a.\bar b.\bar c)+(a.b.c)$
$s = (\bar a . (\bar b + (\bar a.b.\bar c)) . c + (\bar a.b.\bar c))$

| $i_3$ | $i_2$ | $i_1$ | $i_0$ | $a$ | $b$ | $c$ | $d$ | $e$ | $f$ | $g$ |
| ----- | ----- | ----- | ----- | --- | --- | --- | --- | --- | --- | --- |
| 0     | 0     | 0     | 0     | 1   | 1   | 1   | 1   | 1   | 1   |     |
| 0     | 0     | 0     | 1     |     | 1   | 1   |     |     |     |     |
| 0     | 0     | 1     | 0     | 1   | 1   |     | 1   | 1   |     | 1   |
| 0     | 0     | 1     | 1     | 1   | 1   | 1   | 1   |     |     | 1   |
| 0     | 1     | 0     | 0     |     | 1   | 1   |     |     | 1   | 1   |
| 0     | 1     | 0     | 1     | 1   |     | 1   | 1   |     | 1   | 1   |
| 0     | 1     | 1     | 0     |     |     | 1   | 1   | 1   | 1   | 1   |
| 0     | 1     | 1     | 1     | 1   | 1   | 1   |     |     |     |     |
| 1     | 0     | 0     | 0     | 1   | 1   | 1   | 1   | 1   | 1   | 1   |
| 1     | 0     | 0     | 1     | 1   | 1   | 1   | 1   |     | 1   | 1   |
$b=\overline{\bar i_3.i_2.\bar i_1.i_0}.\overline{\bar i_3.i_2.i_1.\bar i_0} = i_3+\bar a_2+\overline{a_1\oplus a_0}$ (à refaire)
$c=\overline{\bar i_3.\bar i_2.i_1.\bar i_0}$

$C_{out,n-1} \neq C_{out,n-2}$

| $C_{out,n-1}$ | $C_{out,n-2}$ | v   |
| ------------- | ------------- | --- |
| 0             | 0             | 0   |
| 0             | 1             | 1   |
| 1             | 0             | 1   |
| 1             | 1             | 0   |

| $v$ | $i$ | $r$ |
| --- | --- | --- |
| 0   | 0   | 0   |
| 0   | 1   | 1   |
| 1   | 0   | 1   |
| 1   | 1   | 0   |