1. Fundamentals of Computer Science Part i2
Fundamentals of Computer Science i2 (MZK 2002/03)
Fundamentals of Computer Science Part i2
Lecture 3
Digital Logic
15 November 2018
Lecture 02 I/O Devices and Networks

2. Topics for this lecture
Gates and Boolean logic
AND, OR, NOT, NAND, …
Integrated circuits
SSI,MSI,LSI,VLSI
Memory
Flip-Flop
Arithmetic
Half-adder, Full-adder
15 November 2018

3. Microprocessor core layout
AMULET3, being designed at the University of Manchester.
Low power, high performance, asynchronous, ARM compatible.
Size 3mm x 1mm.
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4. Basics of hardware design
Components in the picture
data path (bottom strip), register bank (centre)
ALU, adder, multiplier, instruction controller, ...
The lowest logical design level
gates built from transistors
circuits built from gates (arithmetic, memory)
Device level, physics...
N/P-type semiconductors (transistors)
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5. Digital circuits Two values only, 0 and 1 Gates
continuous voltage range (within bounds)
0 is low signal (voltage range 0 to 1)
1 is high signal (voltage range 2 to 5)
Gates
electronic devices that compute functions of 0/1
made from transistors (very fast & small switches)
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6. How a transistor works...
When input voltage below threshold, no current flows through; then output voltage high
When input voltage above threshold, current flows through; then output voltage low
Note signal is inverted, hence a NOT gate
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7. The three main gates NOT invert (negate) single input.
A, B inputs X output
X = f(A,B)
(truth table)
NOT invert (negate) single input.
AND 1 only if both inputs 1
OR 1 if at least one input 1
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8. Two more gates Simpler - 2 instead of 3 transistors... NAND
0 only if both inputs 1 (inverted AND)
NOR
0 if at least one input 1
(inverted OR)
Simpler - 2 instead of 3 transistors...
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9. Boolean algebra Can have functions of N variables, eg Write
M = f (A,B,C)
Write
AB for A AND B
A+B for A OR B
for NOT A
Write functions as expressions
M = BC + A C + AB + ABC (majority vote)
Laws to identify equivalent functions, eg
A + BC = (A+B)(A+C) A = 0 A A B C A
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10. More gates (NAND) Simpler - one type of gate…
NAND is complete (any circuit can be created from it)
Question: Can you do NOT?
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11. More gates (XOR) XOR is eXclusive OR 1 only if exactly one input is 1
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12. Integrated circuits (chips)
SSI chip
5mm x 5mm
Standardised
Pins
Classification based on number of gates:
from Small Scale Integrated (SSI), 1-10 gates,
to Very Large Scale Integrated (VLSI), > 100,000 gates
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13. Types of chips Combinational circuits Memories Arithmetic Control
Boolean functions, transform inputs to output
Memories
can store bits; contain feedback
Flip-Flop
Arithmetic
Half-adder, Full-adder
Control
data buses, clocks, etc
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14. Clock signals Clock is a circuit that emits a series of pulses.
Interval between pulses = clock cycle time
Usually detect rising/falling edge
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15. The Flip-Flop Also called a clocked D latch
Has inputs D and clock, and output Q
When control is on, Q = D
When control is off, output cannot change, & hence D stored
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16. Memories Registers Memories N-bit flip-flop gives N-bit register
N bits = one word
Memories
M registers gives M-word memory
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17. Arithmetic Addition Adders
1-bit addition yields 1-bit result and 1-bit carry
0 + 0 = 0
0 + 1 = 1
1 + 0 = 1
1 + 1 = 0 carry 1
Adders
half-adder = 1-bit adder with 2 bit input
full-adder = 1-bit adder with additional carry input
N-bit adder requires N full-adders
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18. Half-adder 2 bits on input 1 bit sum plus 1 bit carry on output
Cannot handle carry in the middle of the word...
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19. Full-adder Built from two half-adders 2 bits and carry on input
1 bit sum plus 1 bit carry on output
Can be strung together into N-bit carry, ripple effect
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20. Summary Arithmetic Logic Unit Data bus More complex circuits
similar to adders
Data bus
transfers data along wires, one wire per bit
using control signals (clocks)
More complex circuits
design in Boolean algebra
build from standard chips or produce VLSI
15 November 2018