LESSON 3: PERFORMING MENSURATION AND CALCULATION LO 1. Select measuring instruments LO 2. Carry out measurements and calculation LO 3. Maintain measuring instruments Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 1 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. Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 2 Below is the list of all the standard units of measurement used for data storage. Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 3 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. Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 4 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. Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 5 Decimal Number Quotient Remainder Binary Code: __________________________________ Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 6 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. Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 7 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. Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 8 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 Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 9 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. Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 10 Table 3.5: System International (SI) and Binary Prefixes Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 11 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. Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 12 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 Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 13 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? Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 14 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? Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 15 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? Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 16 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? Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 17 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 Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 18 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. Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 19 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. Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 20 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 Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 21 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 Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 22 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. Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 23 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 Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 24 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. Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 25 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. Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 26 Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 27 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. Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 3. Eye glasses 28 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. Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 29 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). Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 30 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. Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 31 Sample Problem 2: Compute the amount of electric current flowing through the circuit. 220v 900 Ω Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 32 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 Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 33 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. Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 34 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. Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 35 SERIES AND PARALLEL CIRCUIT Electrical loads can be connected in series, parallel or complex connection. SERIES CONNECTION PARALLEL CONNECTION Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin COMPLEX CONNECTION 36 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) Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 37 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 Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 38 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 Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 39 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) - + Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 40 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 Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 10 Ω 41 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 Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 42 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. Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 43 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. Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 44 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 Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 45 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 Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 46 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=? Author: Joel Tiemsin / YouTube Channel: Joel Tiemsin 47