Download 2 to its decimal equivalent

Digital Electronics
Digital circuits work on the basis of a transistor being used as a switch. Consider a light
switch, a transistor can be considered almost the same and in some circuits transistors are
used to control large amounts of power with very little input power being used.
In the first circuit if there is no voltage applied to the base of Q1 then it is not switched "on" and
accordingly the + 5V passing through the 10K load resistor from our + 5V supply appears at both
the collector of the transistor and also at output 1.
If we apply + 5V to the base of Q1 then because it is greater than 0.7 V than the grounded
emitter Q1 will switch on just like a light switch causing the + 5V from our supply to drop entirely
across the 10K load resistor. This load could also be replaced by a small light bulb, relay or LED in
conjunction with a resistor of suitable value. In any event the bulb or led would light or the relay
would close.
The output is always the opposite to the input and in digital basics terms this is called an
"inverter" a very important property.
Now looking at Q2 and Q3 to the right of the schematic we simply have two inverters
chained one after the other. Here if you think it through the final output 2 from Q3 will
always follow the input given to Q2. This in digital basics is your basic transistor switch
Logic Blocks in Digital Basics
Depending upon how these "switches" and "inverters" are arranged in integrated circuits we
are able to obtain "logic blocks" to perform various tasks.
In the first set of switches A, B, and C they are arranged in "series" so that for the input to
reach the output all the switches must be closed. This may be considered an "AND-GATE".
In the second set of switches A, B, and C they are arranged in "parallel" so that for any input to
reach the output any one of the switches may be closed. This may be considered an "ORGATE".
in digital logic. If we added "inverters" to either of those blocks, called "gates", then we achieve
a "NAND-GATE" and a "NOR-GATE" respectively.
we have depicted four major logic blocks AND-GATE, NAND-GATE, OR-GATE and NOR-GATE
plus the inverter. Firstly the "1's" and the "0's" or otherwise known as the "ones" and "zeros".
A "1" is a HIGH voltage (usually the voltage supply) and the "0" is no voltage or ground
potential. Other people prefer designating "H" and "L" for high and low instead of the "1's"
and the "0's". Stick with which system you feel most comfortable.
Introduction to Numbering Systems
• We are all familiar with the decimal number
system (Base 10). Some other number
systems that we will work with are:
– Binary  Base 2
– Hexadecimal  Base 16
Significant Digits
Binary: 11101101
Most significant digit
Least significant digit
Hexadecimal: 1D63A7A
Most significant digit
Least significant digit
Binary Number System
• Also called the “Base 2 system”
• The binary number system is used to model the
series of electrical signals computers use to
represent information
• 0 represents the no voltage or an off state
• 1 represents the presence of voltage or an
on state
Binary Numbering Scale
Base 2
Number
Base 10
Equivalent
Power
Positional
Value
000
0
20
1
001
010
011
100
101
110
111
1
2
3
4
5
6
7
21
22
23
24
25
26
27
2
4
8
16
32
64
128
Decimal to Binary Conversion
• The easiest way to convert a decimal number to its
binary equivalent is to use the Division Algorithm
• This method repeatedly divides a decimal number by
2 and records the quotient and remainder
– The remainder digits (a sequence of zeros and ones) form
the binary equivalent in least significant to most
significant digit sequence
Division Algorithm
Convert 67 to its binary equivalent:
6710 = x2
Step 1: 67 / 2 = 33 R 1
Step 2: 33 / 2 = 16 R 1
Step 3: 16 / 2 = 8 R 0
Step 4: 8 / 2 = 4 R 0
Step 5: 4 / 2 = 2 R 0
Step 6: 2 / 2 = 1 R 0
Step 7: 1 / 2 = 0 R 1
Divide 67 by 2. Record quotient in next row
Again divide by 2; record quotient in next row
Repeat again
Repeat again
Repeat again
Repeat again
STOP when quotient equals 0
1 0 0 0 0 1 12
Binary to Decimal Conversion
• The easiest method for converting a binary
number to its decimal equivalent is to use the
Multiplication Algorithm
• Multiply the binary digits by increasing powers
of two, starting from the right
• Then, to find the decimal number equivalent,
sum those products
Multiplication Algorithm
Convert (10101101)2 to its decimal equivalent:
1 0 1 0 1 1 0 1
Binary
Positional Values
Products
x x x x x x x x
27 26 25 24 23 22
128 + 32 + 8 + 4 + 1
17310
21 20
Hexadecimal Number System
• Base 16 system
• Uses digits 0-9 &
letters A,B,C,D,E,F
• Groups of four bits
represent each
base 16 digit
Decimal to Hexadecimal Conversion
Convert 83010 to its hexadecimal equivalent:
830 / 16 = 51 R14
51 / 16 = 3 R3
3 / 16 = 0 R3
= E in Hex
33E16
Hexadecimal to Decimal Conversion
Convert 3B4F16 to its decimal equivalent:
Hex Digits
3
Positional Values
Products
x
B
x
4
x
F
x
163 162 161 160
12288 +2816 + 64 +15
15,18310
Binary to Hexadecimal Conversion
• The easiest method for converting binary to
hexadecimal is to use a substitution code
• Each hex number converts to 4 binary digits
Substitution Code
Convert 0101011010101110011010102 to hex using
the 4-bit substitution code :
5
6
A
E
6
0101 0110 1010 1110 0110 1010
56AE6A16
A