1. Information Storage and Spintronics 02
Atsufumi Hirohata
Department of Electronic Engineering
09:00 Tuesday, 02/October/2018 (J/Q 004)

2. Contents of Information Storage and Spintronics
Lectures : Atsufumi Hirohata P/Z 019)
Advancement in information storages and spintronics (Weeks 2 ~ 9)
[15:00 ~ 16:00 Mons. (J/Q 004) & 09:00 ~ 10:00 Tues. (J/Q 004)]
No lectures on Week 3
Replacements : Week 2, 11:00 on Wed. (SLB 210) & 16:00 on Fri. (J/P 005)
I. Introduction to information storage (01 & 02)
II. Magnetic information storages (03 ~ 08)
III. Solid-state information storages (09 ~ 13)
IV. Memories and future storages (14 ~ 16)
V. Spintronic devices (17 ~ 18)
Practicals :
Analysis on spintronic devices
[Weeks 2 & 4, 09:00 ~ 11:00 Weds. (XRD, P/A ),
Weeks 5 ~ 6, 09:00 ~ 11:00 Weds. (AGFM, P/A 016) &
Weeks 7 ~ 8, 09:00 ~ 11:00 Weds. (MR, P/F 005)]
Continuous Assessment :
Assignment to be handed-in to the General Office (Week 10).

3. Quick Review over the Last Lecture
Von Neumann’s model :
CPU
Input
Output
Working storage
Permanent storage
Bit / byte :
1 bit :
2 1 = 2 combinations
1 digit in binary number
1 byte (B) = 8 bit
Memory access : *

4. 02 Binary Data Binary numbers Conversion Advantages
Logical conjunctions
Adders
Subtractors

5. Bit and Byte
Bit :
“Binary digit” is a basic data size in information storage.
1 bit : 2 1 = 2 combinations ; 1 digit in binary number = = =
: : : :
Byte :
A data unit to represent one letter in Latin character set.
1 byte (B) = 8 bit
1 kB = 1 B × 1024
1 MB = 1 kB × 1024
: :

6. Binary Numbers
The modern binary number system was discovered by Gottfried Leibniz in 1679 : *
Decimal notation Binary notation
: : *

7. Conversion to Binary Numbers 1
For example, 1192 :
2 ) = 20 × 1192
2 ) 586… = 21 × × 0
2 ) 293… = 22 × × × 0
2 ) 146… = 23 × × × × 0
2 ) … = 24 × × × × × 0
2 ) … = 25 × × × × × × 0
2 ) … = 26 × × × × × × 0
+ 20 × 0
2 ) … = 27 × × × × × × 1
+ 21 × × 0
2 ) … = 28 × × × × × × 0
+ 22 × × × 0
2 ) … = 29 × × × × × × 1
+ 23 × × × × 0
2 ) … = 210 × × × × × × 0
+ 24 × × × × × 0
2 ) …1 =

8. Conversion to Binary Numbers 2
For example, 0.1 :
0.1 × 2 = 0.2 <
0.2 × 2 = 0.4 <
0.4 × 2 = 0.8 <
0.8 × 2 = 1.6 >
0.6 × 2 = 1.2 >
0.2 × 2 = 0.4 <
: : =

9. Why Are Binary Numbers Used ?
In order to represent a number of “1192” by ON / OFF lamps :
Binary number : (11 digits = 11 lamps)
Decimal number : (4 digits × 9 = 36 lamps)
Similarly, Ternary number : (7 digits × 2 = 14 lamps)
1192 =
= 36 × × × × × × × 1
Quaternary number : (6 digits × 3 = 18 lamps)
1192 =
= 45 × × × × × × 0
Binary numbers use the minimum number of lamps (devices) !

10. Mathematical Explanation
In a base-n positional notation, a number x can be described as :
x = n y (y : number of digits for a very simple case)
In order to minimise the number of devices, i.e., n × y,
ln(x) = y ln(n)
Here, ln(x) can be a constant C,
C = y ln(n)
y = C / ln(n)
By substituting this relationship into n × y,
n × y = C n / ln(n)
To find the minimum of n / ln(n),
[n / ln(n)]’ = {ln(n) – 1} / {ln(n)} 2
Here, [n / ln(n)]’ = 0 requires
ln(n) – 1 = 0
Therefore, n = e (= …) provides the minimum number of devices.

11. Logical Conjunctions 1 AND : Venn diagram of A∧B Truth table Input
Output A B
A∧B
True (T) (1)
T (1)
False (F) (0)
F (0)
Logic circuit *

12. Logical Conjunctions 2 OR : Venn diagram of A∨B Truth table Input
Output A B
A∨B
T (1)
F (0)
Logic circuit *

13. Logical Conjunctions 3 NOT : Venn diagram of ¬A (Ā) Truth table Input
Output A Ā
T (1)
F (0)
Logic circuit *

14. Additional Logical Conjunctions 1
NAND = (NOT A) OR (NOT B) = NOT (A AND B) :
Venn diagram of A↑B
Truth table A B
Input
Output A B
A↑B
T (1)
F (0)
Logic circuit *

15. Additional Logical Conjunctions 2
NOR = NOT (A OR B) :
Venn diagram of A¯B
Truth table A B
Input
Output A B
A¯B
T (1)
F (0)
Logic circuit
NOR can represent all the logical conjunctions :
NOT A = A NOR A
A AND B = (NOT A) NOR (NOT B) = (A NOR A) NOR (B NOR B)
A OR B = NOT (A NOR B) = (A NOR B) NOR (A NOR B) *

16. Additional Logical Conjunctions 3
XOR = Exclusive OR :
Venn diagram of A⊕B
Truth table A B
Input
Output A B
A⊕B
T (1)
F (0)
Logic circuit *

17. Half Adder Simple adder for two single binary digits :
XOR for the sum (S)
AND for the carry (C), which represents the overflow for the next digit
Truth table
Input
Output A B S C 1 *

18. Full Adder
Adder for two single binary digits as well as values carried in (C in) :
2 half adders for sum (S)
Input
Output A B
C in S
C out 1
Additional OR for the carry (C out),
which represents the overflow
for the next digit
Truth table *

19. Half Subtractor
Simple subtractor for two single binary digits, minuend (A) and subtrahend (B) :
XOR for the difference (D) B D A
Bor
NOT and AND for the borrow (Bor), which is the borrow from the next digit
Truth table
Input
Output A B D
Bor 1 *

20. Full Subtractor
Subtractor for two single binary digits as well as borrowed values carried in (Bor in) :
2 half subtractor for difference (D)
Input
Output A B
Bor in D
Bor out 1
Additional OR for the borrow (Bor out),
which is the borrow from the next
digit
Truth table *

21. Information Processing
For data processing, two distinct voltages are used to represent “1” and “0” :
Low level (1) and high level (2) voltages
Voltages used :
Devices
Low voltage
High voltage
Emitter-coupled logic (ECL)
- 5.2 ~ V
0 ~ 0.75 V
Transistor-transistor logic (TTL)
0 ~ 0.8 V
2 ~ 4.75 (or 5.25) V
Complementary metal-oxide-semiconductor (CMOS)
0 ~ V DD / 2
V DD / 2 ~ V DD
(V DD = 1.2, 1.8, 2.4, 3.3 V etc.) *

22. Emitter-Coupled Logic
In 1956, Hannon S. Yourke invented an ECL at IBM : *
High-speed integrated circuit, differential amplifier, with bipolar transistors *

23. Transistor-Transistor Logic
In 1961, James L. Buie invented a TTL at TRW : *
Integrated circuit, logic gate and amplifying functions with bipolar transistors *

24. Complementary Metal-Oxide-Semiconductor
In 1963, Frank Wanlass patented CMOS : *
Integrated circuit with low power consumption using complementary MOSFET *