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DIGITAL ELECTRONICS
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OVERVIEW
– electronic circuits capable of carrying out logical (boolean) and arithmetic operations on information stored as binary numbers.
– referred to as digital electronic circuits or logic circuits
– Digital implies that the circuits are operating on numbers or digits, and "logic" implies that the circuits carry out logical or boolean operations.
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OVERVIEW
– information processed by digital electronic circuits is in the form of electrical, binary signals.
– Signals are voltage levels, there are two possible values that they may have.
– Most common systems use voltages of less than 1 volt to represent a 0 (False, Off), and voltages in the range of 3.5 to 5 volts to represent a 1 (True, On).
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OVERVIEW
integrated circuits - chips • a number of circuits all on one device
– small-scale integrated circuits (SSI), less than 100 components
– medium-scale (MSI), up to a thousand components
– large-scale (LSI), up to a hundred thousand components
– very-large scale (VLSI), up to a million components
– super-large scale (SLSI), more than a million components
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LOGIC GATE OPERATION
– Digital circuits that are used to carry out Boolean logic operations are referred to as gates.
– They perform a set of three basic operations from which all the other circuits can be developed.
– Gates are manufactured as chips with a number of gates of a particular type on a chip.
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AND Gate
– The AND gate is a gate whose output is a 1 only if all of it's inputs are 1's. In the case of a 2-input gate as illustrated, the output C is a 1 only if both A and B are 1's.
– This is stated arithmetically as:
C = A · B
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Two Input AND Gate
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– The truth table for the gate is:
A B C0 0 00 1 01 0 01 1 1
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THE OR GATE
– The OR gate is a gate whose output is a one if any of it's inputs are one. In the case of a 2-input gate as illustrated, the output C will be a 1 if either A or B or both A and B are 1's. This is stated arithmetically as:
C = A + B
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OR Gate
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– The truth table for the OR gate is:
A B C0 0 00 1 11 0 11 1 1
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THE INVERTER (NOT GATE)
– The Inverter is a single input gate whose output is the inverse or opposite of it's input. arithmetically this is stated as:
B = A
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NOT Gate
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– The truth table of the inverter is:
A B
0 1
1 0
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THE EXCLUSIVE OR GATE
– The Exclusive OR gate is a gate whose output is a 1 if either of it's inputs is a one, but not if both of them are ones. Arithmetically this is stated as:
C = A B
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– The truth table for the Exclusive OR gate:
A B C0 0 00 1 11 0 11 1 0
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NEGATIVE OUTPUT GATES
• There are two other major gates that are effectively created by adding an inverter to the outputs of the AND and OR gates.
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THE NAND GATE
– The NAND gate is a gate whose output is a 0 only if all of it's inputs are 1's. Arithmetically this is stated as:
C = A · B
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The NAND Gate
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– The truth table for the NAND gate:
A B C0 0 11 0 10 1 11 1 0
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THE NOR GATE
– The NOR gate is a gate whose output is a 0 if any of it's inputs are 1's. Arithmetically this is stated as:
C = A + B
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NOR Gate
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– The truth table of the NOR gate:
A B C0 0 10 1 01 0 01 1 0
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DEMORGAN'S THEOREMS
– Demorgan's theorems are very useful to us as we analyze and describe logic circuits. They simplify expressions in which the product or sum of variables is complemented.
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DEMORGAN'S THEOREMS
A . B = A + B
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DEMORGAN'S THEOREMS
A + B = A · B
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Digital Adders
• Adders are a major function of a computer.– Found in the Central Processor Unit in the Arithmetic Logic area.
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Half-Adder
A
B
Carry
Sum
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Full Adder
A
B
Carry
SumCarry In
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Decoding Circuits
• Have to be able to decode particular combinations of signals.– Used to transfer data from or to memory or peripherals.
– Need to decode the address lines to determine where the data is to go.
– Take a number of input signals and provide enough outputs to indicate what the input was.
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Decoding Circuits
• If the input is two binary signals, there would have to be four outputs.
• One output for each input combination.
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Two Bit Decoder, 74139
D0
D1
3
2
1
0
D1 D0 0 1 2 3
0 0
0 1
1 0
1 1
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Data Selector (Multiplexer)
• Combination of decoder and bus enable logic
• Used when a number of different signals have to be gated to a bus.
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Data Selector
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Data SelectorI0
I1
I2
I3
S1
S0
OUT
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Data Selector
• Above circuit would have to be repeated 32 times for a 32-bit bus.
• 74157 is example of choosing only one of two lines to be transferred with the circuit being duplicated four times on the same chip.
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FLIP-FLOPS
• Basic logic circuit used to store binary information.
• Forms basis of circuits used to create timing and counting signals.
• Foundation for memory and a major component in processor registers.
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FLIP-FLOPS• F/F remember a binary value.• Said to be “Set” when a 1 has been stored.
• Said to be “Cleared” when a 0 has been stored.
• Most often a signal, usually the computer clock signal, is used to tell F/F to store a value.
• Output from circuit is Q, sometimes its compliment is also present.
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Clocked S-R Flip-Flop
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D-TYPE FLIP-FLOP
• Simplified input.• Does not allow F/F to be set and cleared at the same time.
• Needs a clock signal to be set or cleared.
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D-TYPE FLIP-FLOP
Q
Q
D
CLK
PRE
CLR
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D-TYPE FLIP-FLP
• PRE and CLR are used to set and clear the F/F without a clock signal.
• A ‘0’ on PRE would set F/F• A ‘0’ on CLR would clear F/F
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D-TYPE FLIP-FLOP
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J-K FLIP-FLOP
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J-K FLIP-FLOP
• Differs from D and S-R F/F in following ways:– Changes state on falling edge of clock signal.
– Toggles when J and K are high.– J corresponds to S, K corresponds to R.
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REGISTERS
• Used to store binary data.• Similar to a memory location but normally in the processor.
• Consists of a number of F/F whose inputs represent the digits of a binary number.
• Data is loaded into all F/F of register simultaneously by a clock input.
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REGISTERS
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COUNTERS
• Used to count clock pulses at the clock inputs.
• How high the counter counts depends on the number of F/F in counter.
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TWO-BIT COUNTER
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TWO-BIT COUNTER
1 2 3 4 5 6
F/F 1
F/F 2
01
0
01
1
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