1. Logic Gates Flip-Flops Registers Adders
Digital Electronics
Logic Gates
Flip-Flops
Registers
Adders
Jordan Nash - Microprocessor Course

2. Numbers in a computer:
In the Microprocessor and memory Bits are stored electronically
Each bit is represented by an electrical signal which is either a high or low voltage level.
high  1 and low  0
high  0 and low  1
Normal
Logic
Inverse
Logic
Jordan Nash - Microprocessor Course

3. Transistor Transistor
High and Low
Transistor Transistor
Logic (TTL)
NO MAN’S LAND
74LSxx
0.8 – 0.4 Volts
2.0 – 2.4 Volts
CMOS
NO MAN’S LAND
74HCxx
0.1 – 1.0 Volts
3.5 – 4.9 Volts
1:‘High’
0:‘Low’
It is actually a bit more complicated than this since there are different thresholds
for inputs and outputs and their noise margins (indicated here in RED)..
Jordan Nash - Microprocessor Course

4. Making a Zero or and One How do you actually make a 0 or 1 ?
It is clear that depending upon the position of the J1 switch the line will be either ‘0’ or ‘1’
Jordan Nash - Microprocessor Course

5. Binary Logic
Once the bits are stored, we want to be able to perform various operations on the bits
The operations which the microprocessor carries out can all be constructed with a few simple circuits
The basic building blocks are logic “gates”
Jordan Nash - Microprocessor Course

6. Binary Logic truth tables
You may remember from the first year lab the gates AND, OR, NOT
Any digital device can be made out of either ORs and NOTs or ANDs and NOTs. A B
AND 1 A B OR 1 A
NOT 1
Jordan Nash - Microprocessor Course

7. DeMorgan’s Theorem
You can swap ANDs with ORs if at the same time you invert all inputs and outputs :
Exercise: Write truth table for both and prove that this is correct
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8. An AND out of NOTs and ORs
Exercise: Test the claim that you can make any logic device exclusively out of NOTs and ORs by making an AND out of NOTs and ORs:
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9. Answer:
Show that this device has an identical truth table as the AND gate.
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10. Exercise: Exclusive OR
Construct an exclusive OR (XOR) gate using OR, ANDs, and NOT: A B
XOR 1
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11. The Exclusive OR
Solution:
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12. Storing Zeros and Ones: Registers
Registers are electronic devices
capable of storing 0’s or 1’s
D-FLIP-FLOPs are the most elementary registers
can store one bit
8 DFFs clocked together make a one byte register
Capable of storing 8 bits
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13. SR Latch: Set and Reset Gate level design of an SR latch
When S* is low and R* High, Q is high (Set)
When S* is high and R* is low Q is cleared (Reset)
Q and Q* are complements S* R* Q Q* 1
Jordan Nash - Microprocessor Course

14. SR Latch: Hold Gate level design of an SR latch
When S* and R* are high both states for Q are possible (and stable)
The latch remembers the last state it was in, and holds Q in that state
Gate level design of an SR latch S* R* Q Q* 1
Jordan Nash - Microprocessor Course

15. SR Latch: Don’t do this…
When S* and R* are low Q and Q* are no longer complementary
The latch can also enter a race condition where it oscillates
Gate level design of an SR latch S* R* Q Q* 1
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16. SR Latch: 1 bit memory Gate level design of an SR latchQ Q* H L
Ambiguous but stable
Gate level design of an SR latch
S/R high is ambiguous, but stable
This circuit “remembers” that S went low
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17. Gated D Latch Ensures that S and R are always complementary.
When the Clock is high – D is set on the outputs of the latch and it is held there when the clock is low
Exercise: Fill out the truth table for this circuit.
Jordan Nash - Microprocessor Course

18. D latch timing
The input Data to the gated D latch appears on the output (Q)while the clock is high.
Sometimes we want to transfer the data into the register only at a specified moment (for example when the clock changes)
The D Flip-Flop uses two d-latches to latch the data on the edge (depending on the design either positive or negative) of the input clock
Jordan Nash - Microprocessor Course

19. Master Slave – D Flip Flop
Data is stored in the “Master” latch (Qm) when the clock is high
When the clock goes from high to low
The data is held in the Master
The Data is stored in the slave latch output
The Qs output can only change when the clock goes from high to low
Jordan Nash - Microprocessor Course

20. A real D-Flip-Flop (DFF)
CLK D S R Q
Q-bar X L H 
One can Set or Reset (Clear) the DFF using S or R
When S and R are High, on the rising edge of the clock the data are transferred and stored in Q.
Jordan Nash - Microprocessor Course

21. A register that stores 4 bits
4-bit Register
A register that stores 4 bits
Data Stored on rising edge of clock in
Q0,Q1,Q2,Q3
Data coming in
D0,D1,D2,D3
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22. Byte Register 8 bit register in a single package 74F574
Byte coming in
8 bit register in a single package
74F574
Also contains tri-state outputs
CLK
Byte Stored
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23. Addition with Binary Logic Gates
Computers carry out addition with binary addition of bits stored in registers
We can build additions of large numbers of bits out of units which add two bits
$3+$4
$3+$C
$D+$4
$D+$C
0011
1101
+ 0100
+ 1100
= 0111
= 1111
=10001
=11001 $7 $F
$11
$19
Example: Adding two 4 bit numbers results in a 4 bit number plus one carry bit or effectively a 5 bit number
Lets construct this adder from gates
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24. Additions of two bits: The half adder
Adding two bits generates two bits of output
1 “Sum Bit” S
1 “Carry Bit” C
The truth table for this operation is shown along with an implementation using two gates A B C S 1
Jordan Nash - Microprocessor Course

25. Full Adder
In order to add larger numbers, we need to be able to bring the carry from the lower order bits, and add this to the sum
The inputs are:
the two bits to be added (A,B)
The Carry Bit (C)
The outputs are:
The Sum Bit (S)
The Carry Out Bit (C+)
We can build this from two half adders and an XOR gate A B C C+ S 1
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26. Two bit adder
We can construct logic that adds more than 1 bit together by using multiple full adder circuits
Exercise:
Construct a circuit that adds two two bit words (Ao,A1) and (B0,B1) and produces three Sum Bits (S0,S1,S2)
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27. Solution
With the Full adder building block we can generalize to produce a circuit which adds larger numbers
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28. Four plus Four bit addition
This can clearly be generalized to any number of bits
There is a problem in building circuits this way as the carry bits need to propogate through the circuit before the answer is correct
There are other ways to construct adder circuits which avoid this problem
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29. Arithmetic Logic Unit (ALU)
Centre of every computer
Composed of building blocks we have been learning about
Adders
Flip Flops
Registers
We also need to have a data bus to move data in and out - we will learn about this soon
Jordan Nash - Microprocessor Course