I. Digital arithmetic
II. complex digital circuits
III TTL and CMOS technology
IV Microprocessors
V. Memory chips
VI Motherboards
I. Digital arithmetic
1. Positional number system
binary
hexadecimal
decimal
BCD
2. Arithmetic operations on binary numbers
3. Algebra of logic
4. Logic punctuators
II Assumed digital circuits
1. aggregators
2. comparators
3. interrupters
4. counters
5. records
III TTL and CMOS technology
IV Microprocessors
1. microprocessor design
2. types of microprocessors
V. Memory chips
1. RAM
2. ROM
VI. motherboards
1. Processors
2. Chips
3. Magistrals
4. BIOS
Literature
1. "Computer Technology Devices" part. 1 and 2 Krzysztof Wojtyszkiewicz
2. "Urządzenia Techniki Komputerowej" Zdzisław Kolan
Digital Signal - takes a finite sequence of values (digital technology)
0101010101 - writing is called encoding, it is a code word.
Positional number systems - In a code word representing a decimal number, each character represents a well-defined position.
1464 = 1 - 103 + 4 - 102 + 6 - 101 + 4 - 100
136,02 = 1 - 102 + 3 - 101 + 6 - 100 + 0 - 10-1 + 2 - 10-2
L(6) = bn-1-2n-1+6n-2-2n-2+. . . +b222+b121+b020
2. Base of the code, exponent of the power - weight of the code
L(6) = 6323+b222+b121+b020
L(6) = b3-8+b24+b24+b12+b0
Number Systems
b3
b2
b1
b0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
3
0
0
1
1
4
0
1
0
0
5
0
1
0
1
6
0
1
1
0
7
0
1
1
1
8
1
0
0
0
9
1
0
0
1
10
1
0
1
0
11
1
0
1
1
12
1
1
0
0
13
1
1
0
1
14
1
1
1
0
15
1
1
1
1
64 32 16 8 4 2 1
1101110(2) = 110(10)
1101011(2) = 107(10)
342(10) /2 = 171 r 0
171 /2 = 85 r 1
85 /2 = 42 r 1
42 /2 = 21 r 0
21 /2 = 10 r 1
10 /2 = 5 r 0
5 /2 = 2 r 1
2 /2 = 1 r 0
1 /2 = 0 r 1
342(10) = 101010110
"BCD" code Hexadecimal code
decimal
hexadecimal
0
0
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
A
11
B
12
C
13
D
14
E
15
F
Complex digital circuits
An integrated circuit - a microcircuit is a micro-electronic functional circuit in which a component is made by a single technology.
Semi-conductor integrated circuit - is an integrated circuit whose components are made in inert and on the surface of a silicon substrate.
Semi-conductor structure - is a transistor , diode or half-conductor integrated circuit without resistance.
Types and properties of semiconductor digital integrated circuits - the operations of logic (digital) circuits can be boiled down to a few basic logic functions otherwise reflowing.
These functions are realized by electronic circuits called gates otherwise known as functors are gates realize logic functions.
Logical products or logical sums
end, or not
For descriptions of logical variables, 0 or 1 will be used.
There are two voltage levels:
low (low)
high level (height)
Assigning binary (binary) values are 0 and 1.
The type horizontally is completely arbitrary.
1
0
0
In an arbitrary arrangement
0
0
1
In negative logic
Figure 1 representation of the numbers 0 and 1 in practice, instead of two levels, tolerance fields are defined inside which should be mapped in positive (positive logic) the lower level is assigned the number 0, and the higher 1.
In negative logic, the opposite is true.
Integrated circuit - a microcircuit is a micro-electronic functional circuit in which the components and connecting wires are made by a single technology.
Semi-conductor integrated circuit - is an integrated circuit whose components are made in a volume and on the surface of a silicon substrate.
Semi-conductor structure - This is a transistor, diode or semi-conductor integrated circuit without a case, resistive.
Types and properties of semiconductor digital integrated circuits - the operations of logic (digital) circuits can be reduced to a few basic overflow functions. These functions are performed by electronic circuits called gates otherwise known as functors, logic elements . The basic functors are gates that implement logic functions.
Number Systems:
In the digital number system, a very important role is played by two-, eight- and sixteen-element sets which are named after the system, respectively.
Of the sets listed above, the binary set plays the most important role because the basic system is binary in nature.
The way of writing a number is called positional. When the value of digits depends on the place that is, the position that this digit occupies each position has a specific and non-variable digital value.
Denote any number system by a small "p" and any N integer can be represented as a series: an-1 pn-1+an-2pn-1+. . . +a1p1+a0p0=∑n-1 i=0 a1p1
The B number system with base "p" uses digits from 0 to p-1
The following table shows the digits used in the systems.
p = 2,3,8,10,12,16
You will notice that for p>10 additional characters should be derived.
p
Number system
Used digits
2
Binary/binary
0,1
3
Triple/teranary
0,2,3
8
Eight/odal
0,1,2,3,4,5,6,7
10
Decimal/decimal
1,2,3,4,5,6,7,8,9,0
12
Duodecal/duodecinal
0,1,2,3,4,5,6,7,8,9,A,B
16
Hexadecimal/hexadecimal
0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F
In a decimal number system, the basis of the system is p=10.
A number in the decimal system (N=10) consisting of the N part of the integer and the fractional part.
Presented as’
[an-1,an-2,. . . ,a1a0,a-1,. . . ,an] 10
where
a1 {0,1,2,3,4,5,6,7,8,9}
has a value:
N10=an-110n-1+an-210n-2+. . . +a1102+a0101+. . .
Decimal system
Twin system
Decimal system
Hexadecimal system
0
0
0
0
1
1
1
1
2
10
2
2
3
11
3
3
4
100
4
4
5
101
5
5
6
110
6
6
7
111
7
7
8
1000
10
8
9
1001
11
9
10
1010
12
A
11
1011
13
B
12
1100
14
C
13
1101
15
D
14
1110
16
E
15
1111
17
F
16
1000 0
18
10
17
1000 1
19
11
18
1001 0
20
12
19
1001 1
21
13
20
1010 0
22
14
100
1100 100
23
64
1000
1110 1000
24
3E8
Example:
574. 28(10) – it is an abbreviated record
(5x102)+(7x101)+(4x100)+(2x10-1)+(8x10-2)
Dual Number System:
This is the simplest positional record.
The elements of the system character set are a pair of digits 0 and 1.
A binary digital is often called a BIT.
In the binary number system p=2 is a number in the binary number system (N2) consisting of a digital integer.
[an-1,an-2,. . . ,a1a0,a-1,a-2,. . . ,a-n]2
Where:
a1 {0. 1}
has values:
N2=an-12n-1+an-22n-2+. . . +a1-21+a220+a12-1+a22-2+. . . +a-n2-n=∑n-1 1-n a1a1
1001 11012
(1x23)+(0x23)+(0x21)+(1x20)+(1+2-1)+(1x2-2)+(0x2-3)+(1x2-4)=2,8125(10)
The above example can be used as an illustration of a binary number to its equivalent decimal. Converting a binary decimal can be done by multiple action on 2 integer parts and multiplying by 2 fractional decimal parts:
10=9. 8125
9 = 2 = 4 rest 1
4 = 2 = 2 rest 0
2 = 2 = 1 = rest 0
1 = 0 = 0 rest 1
Number system Octagon:
p=28
digital: 0,1,2,3,4,5,6,7
Example:
673. 12(8)
(6x82)+(7x81)+(3x80)+(1x8-1)+(2x8-2)
N10=443. 15625
443 : 8 = 55 rest 3
55 : 8 = 6 rest 7
6 : 8 = 0 remainder 6
0,15625 x 8 = 1,25000 = 0,25000 rest 1
0,25000 x 8 = 200000 rest 2
0. 15625(10)=0. 12(8)
Conversion result: 673,12(8)
Hexadecimal Number System:
n=24
0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F
2527 : 16 = 157 rest 1510=F
157 : 16 = 9 rest 1320 = D
9 : 16 = rest 9r = 9
Boolean Algerba:
1. Logical product:
F = AxB = 1 <=> = 1^B = 1
A
B
F
0
0
0
0
1
0
1
0
0
1
1
1
2. Logical sum:
F = A+b = 1 <=> A = 1vB = 1
A
B
F
0
0
0
0
1
1
1
0
1
1
1
1
3. Negotiations:
F = A = 1 <=> A = 0
A
F
0
1
1
0
Laws of Boole's Algebra:
1. For the product of logic:
alternation law AxB = BxA
communication law Ax(BxC) = (AxB)xC
law of separation Ax(BxC) = AxB+AxC
De`Morgan law AxB = A+B
2. For the logical sum:
law of alternation A+B = B+A
communication right A+(B+C) = (A+B)+C
law of separability (A+B) x (A+C) = A+BxC
De`Morgan law A+B = A+B
Logical Identities
Product: Sum:
A x 0 = 0 A + 0 = A
A x 1 = A A + 1 = 1
A x A = 0 A + A = A
A x A = A A + A = 1