Full adder

TopicFull adder

Title

The full adder's truth table

ExampleW04.1

Step1 / 6

Mode

Given

The figure adds three bits $A$ , $B$ and $C_{in}$ with two XOR gates, two AND gates and an OR gate. Fill in its truth table net by net, then read off $S$ and $C_{out}$ for $A = 1$ , $B = 0$ , $C_{in} = 1$ .

Inputs $A$ , $B$ , $C_{in}$ , each $0$ or $1$
$G_1$ , $G_3$ : XOR; $G_2$ , $G_4$ : AND; $G_5$ : OR

Each net in turn, every row of inputs

$A$	$B$	$C_{in}$
0	0	0
0	0	1
0	1	0
0	1	1
1	0	0
1	0	1
1	1	0
1	1	1

Read the circuit

G_1

and

G_3

make the sum,

G_2

and

G_4

the two ways a carry starts, and

G_5

joins them. Work each gate's output net for every row, in the order the signals flow.

Sim

The full adder in the figure

Tap a row of the truth table, or an input, to set $A$ , $B$ and $C_{in}$ . Every wire carrying a $1$ is inked; a $0$ stays in pencil.

Fig.The figure's circuit. A wire carrying a 1 is inked; a 0 stays in pencil.

Inputs

S = 0, Cout = 1

ABCin	S	Cout
	0	0
	1	0
	1	0
	0	1
	1	0
	0	1
	0	1
	1	1

Worked examples

The full adder's truth table

Read the circuit

The full adder in the figure