LESSON 3: PERFORMING
MENSURATION AND CALCULATION
LO 1. Select measuring instruments
LO 2. Carry out measurements and calculation
LO 3. Maintain measuring instruments
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BITS AND BYTES
The smallest unit of measurement used for measuring data is a bit. A
single bit can have a value of either 0 or 1. It may contain a binary value
such as On/Off or True/False.
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Below is the list of all the standard units of measurement used for data
storage.
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CONVERTING DECIMAL NUMBERS INTO BINARY CODES
To convert a decimal number to binary:
• Divide the number to be converted by 2
• Record the quotient and remainder
• Divide the resulting quotient by 2 again.
• Do it repeatedly until the quotient results to 0.
• The remainder which is in the form of 1’s and 0’s is the binary code of
the number. Copy the remainder from bottom to top.
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Example 1: What is the binary code of 12?
As shown in example, the binary code of 12 is 1100 or 00001100 in 8-bits.
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Decimal Number
Quotient
Remainder
Binary Code: __________________________________
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2N PATTERN
The table 3.2 below can also be used to find the 8-bit binary codes of a
number. Start from 1 bit, double the number of patterns (n bit yields 2n
patterns).
PATTERN
Table 3.2: Conversion of decimal number into binary code using 2n pattern.
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Example: What is the binary code of 25?
• Identify the numbers that would give you a total of 25.
• Mark those numbers with “1” and the unused numbers with “0”.
As shown in table below, the binary code of 25 is 00011001. The bits of
“1” and “0” were read from left to right.
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COMPUTER STORAGE AND MEMORY
Computer storage and memory is often measured in megabytes (MB)
and gigabytes (GB). 1 MB of data is 1,024 kilobytes, or 1,048,576
(1024x1024) bytes, not one million bytes, because computers
use binary (base of two) math, instead of a decimal (base of ten)
system.
SD Card
External Hard
Drive
HDD (Hard Disk
Drive)
Thumb Drive
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We count in base 10 by powers of 10:
101 = 10
102 = 10*10 = 100
103 = 10*10*10 = 1,000
Computers count by base 2:
21 = 2
22 = 2*2 = 4
23 = 2*2*2 = 8
210 = 2*2*2*2*2*2*2*2*2*2 = 1, 024
Kilo in base of 10 is 1000.
Kilo in base of 2 is 1024.
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Table 3.5: System International (SI) and Binary Prefixes
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1 TB
1 GB
1 MB
1 kB
1024 GB
1024 MB
1024 kB
1024 B
Table 3.6: Conversion table of bytes into other units.
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CONVERSION OF UNITS
Example 1: 1 GB is equal to how many MB?
(1 GB)(1024) = 1024 MB
1 TB
1 GB
1 MB
1 kB
1024 GB
1024 MB
1024 kB
1024 B
Example 2: 500 GB is equal to how many kB?
(500 GB)(1024)(1024) = 524,288,000 kB
Example 3: 1 MB is equal to how many GB?
(1 MB) / (1024) = 0.00098 GB
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1 TB
1 GB
1 MB
1 kB
1024 GB
1024 MB
1024 kB
1024 B
Convert the following units of measurement:
1.How many bytes are there in 500 MB?
2.How many kB are there in 2 TB storage?
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Convert the following units of measurement:
1.How many bytes are there in 500 MB?
1 TB
1 GB
1 MB
1 kB
1024 GB
1024 MB
1024 kB
1024 B
2.How many kB are there in 2 TB storage?
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CONVERSION OF UNITS
1: 1 TB is equal to how many MB?
(1)(1024)(1024) = 1,048,576 MB
1 TB
1 GB
1 MB
1 kB
1024 GB
1024 MB
1024 kB
1024 B
2: 10 GB is equal to how many kB?
3: 128 GB is equal to how many MB?
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CONVERSION OF UNITS
1: 1 TB is equal to how many MB?
(1)(1024)(1024) = 1,048,576 MB
1 TB
1 GB
1 MB
1 kB
1024 GB
1024 MB
1024 kB
1024 B
2: 10 GB is equal to how many kB?
(10)(1024)(1024) = 10,485,760 kB
3: 128 GB is equal to how many MB?
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CONVERSION OF UNITS
1: 1 TB is equal to how many MB?
(1)(1024)(1024) = 1,048,576 MB
1 TB
1 GB
1 MB
1 kB
1024 GB
1024 MB
1024 kB
1024 B
2: 10 GB is equal to how many kB?
(10)(1024)(1024) = 10,485,760 kB
3: 128 GB is equal to how many MB?
(128)(1024) = 131,072 MB
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INTERNET SPEED
Internet speed is measured in terms of
kbps or Mbps. A lowercase “b” in Mbps
means bits per second while an uppercase
“B” means bytes.
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What are the factors that affect your Internet
speed?
There are several factors that can affect your Internet
speed:
• Internet traffic.
• The server speed of the site you're visiting.
• Your computer's hardware and software
configuration.
• Traffic on your home network.
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COMPUTER MONITOR
Screen Size
To measure a computer screen, measure it diagonally - from the top
left corner to the bottom right corner. It is also important to know the
height and width of the computer screen since not all with the same
computer screen size have the same height and width.
Figure 1. 3:4 ratio computer screen
Figure 2. Wide screen
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MEASURING INSTRUMENT
MULTI-METER OR MULTI-TESTER
Multi-tester is a measuring device used
to measure the amount of electricity in a
circuit or in a voltage source, resistivity of
a material and the continuity of a wire.
Figure 5. Multi-tester or Multi-meter
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SAFE HANDLING PROCEDURES IN USING MULTI-TESTER:
1. Use the multi-tester based on manufacturers intended use of the
device.
2. Set the needle pointer in the correct position before testing.
3. Set the multi-tester to the highest setting when checking unknown
voltages or electric current.
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MULTI-TESTER FUNCTIONS:
First Quadrant: AC voltages
Second Quadrant: DC voltages
Third Quadrant: Electric current
Fourth Quadrant: Resistance
For DC voltages
For AC voltages
For Electric Current
For Resistance
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4. Do not reverse the polarity of the
test probe when checking DC
voltages.
5. Do not connect the multi-tester to
any powered devices if the test knob
is set to resistance (X1, X10, X1K and
X10K)
6. The test probes are color coded.
Black refers to negative and red is
positive.
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7. “Com” in multi-tester plug refers
to “common” or “negative”; “P” is
“positive”.
8. Make sure that the battery that
powers the multi-tester is always
fresh to avoid wrong reading
values when testing.
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Group Activity 3.1 (1/2 CW)
Identify conductors and insulators by using a multi-tester. Use X10K setting.
CONDUCTORS
INSULATORS
1.
2.
3.
4.
5.
Avoid the following:
1. Testing any parts of your body.
2. Testing any powered devices/extension cords, power outlets.
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3. Eye glasses
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OHM’S LAW
Ohm's Law deals with the relationship between voltage and current in
an ideal conductor.
According to Ohm’s Law, at constant resistance, the voltage is directly
proportional to the electric current flowing through the circuit.
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OHM’S LAW
Ohm’s Law is used to compute the unknown quantity in an electric circuit.
I=V/R
According to Ohm’s law, the electric current (I) is directly proportional to
the voltage (v) and inversely proportional to the electrical resistance (R).
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Sample Problem 1. Compute the input voltage provided by the battery
in the circuit below. Let’s presume that the amount of electric current
flowing through the circuit is 0.5 and the load has a resistance of 600
Ohms.
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Sample Problem 2: Compute the amount of electric current flowing
through the circuit.
220v
900 Ω
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Sample Problem 3: How much electrical resistance is needed in the
circuit below given the 12v supply with a current rating of 2A?
2A
12v
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Sample Problem 4: What is voltage requirement of a 1kΩ load? Let’s
assume that the allowable electric current in the circuit is 1.5A.
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Sample Problem 5: If electric current is the one that
causes electric shock, why is it that in danger signs it
was written as, “Danger, High Voltage!” and not
“Danger, High Current!”?
Electric current is the flow of electricity.
Voltage is the source of electricity. It is a stored
energy or defined as the potential difference
between two points – positive and negative.
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SERIES AND PARALLEL CIRCUIT
Electrical loads can be connected in series, parallel or complex
connection.
SERIES CONNECTION
PARALLEL CONNECTION
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COMPLEX CONNECTION
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Series Connection
• In series connection, there is only one path for the electrons to flow.
• Total resistance = sum of the individual resistance in the circuit. (RT = R1 + R2)
• The current drain in every resistor is equal to the total current. (IT = I1 = I2)
• The total voltage is shared among the loads/resistors.
(VT = V1 + V2)
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Parallel Connection
• In parallel connection, there are several paths for the
electrons to flow.
• Total resistance RT can be computer as 1/RT = 1/R1 + 1/R2
• The total current IT in the circuit is shared/divided among
the loads.
I T = I1 + I2
• The voltage drop in every resistor is equal to the total
voltage VT.
VT = V1 = V2
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For resistors in parallel:
• If there are two resistors with different resistance value, then:
RT = R1 x R2
R1 + R2
• If there are two or more resistors with the same value, then:
RT = Value of one resistor
Number of resistors in parallel
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ACTIVITY 4.1:
Let’s see how many circuits can you draw using 3 light bulbs? Please
include the battery in your drawing. (20 points)
-
+
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ACTIVITY 4.2:
How many electric circuits can you make with 3 resistors of the same
resistance? Draw the circuit combinations in 1 whole bond paper.
10 Ω
10 Ω
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10 Ω
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Problem #1: Resistors in Series
Compute the following:
1. Total Resistance
2. Total Voltage
3. Current drain in R1
4. Current drain in R2
5. Voltage drop in R1
6. Voltage drop in R2
Consider the following
values:
R1 = 25 Ω
R2 = 50 Ω
IT = 0.5 A
R1
R2
VT
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Solution to problem #1:
1. RT = R1 + R2
= 25 Ω + 50 Ω
= 75 Ω
The total resistance in the circuit is 75 ohms.
2. VT = (IT)(RT)
= (0.5A)(75 Ω)
= 37.5 v
The total voltage in the circuit is 37.5 volts.
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Solution to problem #1:
3. I1 = IT
= 0.5A
4. I2 = IT
= 0.5A
5. V1 = I1 R1
= (0.5A)(25 Ω)
= 12.5 v
The voltage drop in resistor 1 is 12.5 volts.
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Solution to problem #1:
6. V2 = I2 R2
= (0.5A)(50 Ω)
= 25.0 v
The voltage drop in resistor 1 is 25 volts.
Checking of the total voltage: V1 + V2 = VT
12.5v + 25.0v = 37.5v
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Problem #1: Resistors in Series
• You will notice that in series, the electric current is the same for all
the resistors while the voltage is shared among the loads.
Current drain = 0.5A
R1 = 25 Ω
Current drain = 0.5A
R2= 50 Ω
Voltage drop = 12.5v
VT= 37v
Voltage drop = 25v
Total current = 0.5A
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Problem #2: Resistors in Series
Compute the following:
1.
Total Resistance
2.
Total Voltage
3.
Current drain in R1
4.
Current drain in R2
5.
Current drain in R3
6.
Voltage drop in R1
7.
Voltage drop in R2
8.
Voltage drop in R3
10 Ω
20 Ω
30 Ω
VT=?
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