1. Digital Electronics and Computer Interfacing
Tim Mewes
3. Digital Electronics

2. Digital Electronics and Computer Interfacing
3.5 Adder
An adder is a device that will calculate the sum of two numbers
In digital electronics an adder needs to be able to add two binary numbers
Idea: create an adder for one bit numbers – numbers with more bits can then be added by chaining multiple adders together
Digital Electronics and Computer Interfacing

3. Digital Electronics and Computer Interfacing
3.5.1 Half Adder
Two input bits A and B and two outputs: the sum S and the carry output Co
Truth table
Problem: how to use the carry output for the next bit?!
Digital Electronics and Computer Interfacing

4. 3.5.2 Full Adder Takes three input bits A, B and the input carry Ci
Has again two outputs the sum S and the carry output Co
Truth table
How to add two n-bit numbers?!
Digital Electronics and Computer Interfacing

5. Digital Electronics and Computer Interfacing
3.5.3 Ripple carry adder
Chain multiple 1 bit full adders – each carry bit ripples to the next full adder
1 bit
full adder Ci
A (bit n)
B (bit n) Co
S (bit n)
1 bit
full adder Ci
A (bit 1)
B (bit 1) Co
S (bit 1)
1 bit
full adder Ci
A (bit 0)
B (bit 0) Co
S (bit 0) …
If the most significant bit produces a carry output an overflow has occurred
Digital Electronics and Computer Interfacing

6. 3.6.1 Digital 2 Channel Multiplexer
Multiplexer outputs one of its inputs A or B depending on a third input S A B S Q
S=0 selects A
S=1 selects B
Digital Electronics and Computer Interfacing

7. 3.6 Multiplexer
A multiplexer combines multiple inputs into one single output
What is it good for?
Transmit multiple data streams over one physical link
Practical example: telephone
Synchronized switches
Digital Electronics and Computer Interfacing

8. 3.6.2 Digital 2n channel multiplexer
2n-Channel multiplexer outputs one of its 2n inputs (I0- I2n-1) depending on the n inputs (S0-Sn-1) I0 I1 Q . . .
I2n-1 … S0 S1
Sn-1
Digital Electronics and Computer Interfacing

9. 3.6.2 Digital 2n channel multiplexer
Example n=2  2n=4 Channel multiplexer
X: Don’t care
Digital Electronics and Computer Interfacing

10. 3.6.2 Digital 2n channel multiplexer
A 2n channel multiplexer is more:
You can create any logic function with n inputs!!
Put your own example here
Digital Electronics and Computer Interfacing

11. 3.6.2 Digital 2n channel multiplexer
A 2n channel multiplexer is more:
You can create any logic function with n inputs!!
Example 1: AND I0 S1 Q I1 I2 I3 S0 3V
Digital Electronics and Computer Interfacing

12. 3.6.2 Digital 2n channel multiplexer
Example 2: XOR I0 S1 Q I1 I2 I3 S0 3V
Digital Electronics and Computer Interfacing

13. Precaution: turn fully counter clockwise!
Vcc=5 V
GND
8 Boolean
indicators
7486
horizontal
lines are
connected
74151
Leave in +5 position
8 Boolean
controls
Digital Electronics and Computer Interfacing