basics of digital electronics
TRANSCRIPT
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2
2
+1
=3
HOW THE COMPUTER GETS
THE ANSWER
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A computer understands
information composed of only zeros and
ones.
The decimal number system is
convenient for the programmer.
The computer uses binary digits for its
operation.
01
0
1
1
0
1
1
0
0
1
0
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BASIC NUMBER SYSTEM
DECIMAL
HEXA
DECIMAL
OCTAL
BINARY
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DECIMAL NUMBER SYSTEM
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• 0,1,2,3,4,5,6,7,8,9.DIGITS
• 10BASE
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8*10
9*10
5*104*10
DECIMAL NUMBER 4598
0
1
2
3
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BINARY NUMBER SYSTEM
•0,1DIGITS
•2BASE
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BINARY NUMBER 1011
1*2
1*20*2
1*2
0
1
2
3
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HEXADECIMAL NUMBER
SYSTEM
•0,1,2,3,4,5,6,7,
•8,9,A,B,C,D,E,F.DIGITS
•16BASE
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HEXADECIMAL NUMBER 1A5D
D*16
5*16
A*161*16
0
1
2
3
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OCTAL NUMBER SYSTEM
•0,1,2,3,4,
•5,6,7,8.DIGITS
•8BASE
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OCTAL NUMBER 5273
3*8
7*82*8
5*8
0
1
2
3
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CONVERSIONS IN BASIC
NUMBER SYSTEM
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BINARY TO DECIMAL
• 1 0 1 0 1
BINARY
• 5 4 3 2 1
BIT POSITION • 1*2 +0*2 +1*2
+0*2 +1*2.
MUL WITH BASE
• 21
DECIMAL4 3 2
1 0
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HEXADECIMAL TO DECIMAL
•5A9
HEX
•3 2 1
BIT POSITION• 5*16
+A*16 +9*16
MUL WITH BASE
•1449
DECIMAL2
1
0
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OCTAL TO DECIMAL
•645
OCTAL
•3 2 1
BIT POSITION •6*8 +4*8
+5*8.
MUL WITH BASE
•421
DECIMAL2 1
0
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DECIMAL TO BINARY
• Q=19
• R=139 • Q=9
• R=119 • Q=4
• R=19 • Q=2
• R=04 • Q=1
• R=02 • Q=0
• R=11
LSB MSB
Divide through out by 2
DECIMAL = 39
BINARY = 100111
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DECIMAL TO HEX
• Q=2
• R=335• Q=0
• R=22
Divide through out by 16
LSB MSB
DECIMAL = 35
HEX = 23
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DECIMAL TO OCTAL
• Q=57
• R=5461
• Q=7
• R=157
• Q=0
• R=77
Divide through out by 8
LSB MSB
DECIMAL = 461
OCTAL = 715
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BINARY TO HEXADECIMAL
BINARY
• (010111011001)
4BITS DIV
• (0101)(1101)(1001)
HEX
• (5) (D) (9) =(5D9)2 16
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BINARY TO OCTAL
BINARY
• (101111100)
3BIT DIV
• (101)(111)(100)
OCTAL
• (5) (7) (4) =(574)
2
8
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HEXADECIMAL TO BINARY
HEX
• (5C)
EXPANSION
• (0101)(1100)
BINARY
• (01011100)16 2
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OCTAL TO BINARY
OCTAL
• (436)
EXPANSION
• (100)(011)
BINARY
• (100011)8 2
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HEXADECIMAL TO OCTAL
• (4DF)HEX
• (0100)(1101)(1111)EXP
• (010011010000)BINARY
• (010)(011)(011)(111)3BIT DIV
• (2337)OCTAL
16
2
8
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OCTAL TO HEXADECIMAL
• (456)OCTAL
• (100)(101)(110)EXP
• (100101110)BINARY
• (0001)(0010)(1110)4BIT DIV
• (12E)HEX
8
2
16
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REPRESENTATION OF NEGATIVE
NUMBER
9’S & 10’S COMPLIMENT
• DECIMAL NUMBER SYSTEM
1’S & 2’S COMPLIMENT
• BINARY NUMBER SYSTEM
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BINARY ARITHMETIC
1• BINARY ADDITION
2• BINARY SUBTRACTION
3• BINARY MULTIPLICATION
4• BINARY DIVISION
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0 + 0 = 0
1 + 0 = 1
0 + 1 = 1
1 + 1 = 0 1 (Carry bit)
BINARY ADDITION
1 1 0 1 (13 decimal)
+0 0 0 1 (+1 decimal)
1 1 1 0 (14 decimal)
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BINARY SUBTRACTION
0 ‐ 0 = 0
1 ‐ 0 = 1
0 ‐ 1 = 1 1 (Carry bit)
1 ‐ 1 = 0
1 1 0 1 (13 decimal)
+ 0 0 1 1 (-3 decimal)
1 0 1 0 (10 decimal)
Borrow
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1 0 0 0 =810
X 0 1 1 0 =610
0 0 0 0
+ 1 0 0 0
+ 1 0 0 0
+ 0 0 0 0
0 1 1 0 0 0 0 = 4810
BINARY MULTIPLICATION
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BINARY DIVISION
011 ) 0 1 1 0 0 1 0 ( 1
0 1 1
0 0 0 (0
0 0 0
0 0 0 (0
0 0 0
0 0 1 (0
0 0 0
0 1 0
Q=1000=1610
R=10= 210
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SIGNED ARITHMETIC OPERATION
MSB bit is reserved to represent the sign of
the number.
When the number is negative, the sign bit is
kept one.
When the number is positive, the sign bit is 0.
In 8-bit processor, MSB = sign bit & other 7
bits = number.
In 16-bit processor, MSB = sign bit & other
15 bits = number.
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EXAMPLES
0 0 0 0 0 1 0 1 (+5 decimal)
0 0 0 0 0 1 0 0 (+4 decimal)
0 0 0 0 1 0 0 1 (+9 decimal)
0 0 0 0 0 1 0 1 (+5 decimal)
1 0 0 0 0 0 1 0 (-2 decimal)
1 1 1 1 1 1 0 1 (1’comp of -2)
1 1 1 1 1 1 1 0 (2’s comp of -2)
0 0 0 0 0 0 1 1 (+3 decimal)
1
2
1 2 1
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BCD AND GRAY CODE
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LOGIC GATES
Logic gates perform basic logical functions.
They are fundamental building blocks of
digital integrated circuits.
Most logic gates take an input of two binary
values, and output a single value of a 1 or 0.
Some circuits may have only a few logic
gates, while others, such as microprocessors,
may have millions of them.
There are seven different types of logic gates,
which are outlined.
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FLIP-FLOPS
A flip-flop or latch is a circuit that has two
stable states and can be used to store state
information.
Each flip-flop stores one bit of information
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THANK YOU