Digital Electronics and Computer Interfacing

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Presentation transcript:

Digital Electronics and Computer Interfacing Tim Mewes 3. Digital Electronics

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

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

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

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

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

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

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

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

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

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

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

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