1. Digital Electronics

2. 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.resistor The output is always the opposite to the input and in digital basics terms this is called an "inverter" a very important property.

3. 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

4. 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 "OR- GATE". 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.

5. 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.voltage

6. 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

7. Significant Digits Binary: 11101101 Most significant digit Least significant digit Hexadecimal: 1D63A7A Most significant digit Least significant digit

8. 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

9. Binary Numbering Scale Base 2 Number Base 10 Equivalent Power Positional Value 00002020 1 00112121 2 01022 4 01132323 8 10042424 16 10152525 32 11062626 64 11172727 128

10. 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

11. Division Algorithm Convert 67 to its binary equivalent: 67 10 = x 2 Step 1: 67 / 2 = 33 R 1 Divide 67 by 2. Record quotient in next row Step 2: 33 / 2 = 16 R 1 Again divide by 2; record quotient in next row Step 3: 16 / 2 = 8 R 0 Repeat again Step 4: 8 / 2 = 4 R 0 Repeat again Step 5: 4 / 2 = 2 R 0 Repeat again Step 6: 2 / 2 = 1 R 0 Repeat again Step 7: 1 / 2 = 0 R 1STOP when quotient equals 0 1 0 0 0 0 1 1 2

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

13. Multiplication Algorithm Convert (10101101) 2 to its decimal equivalent: Binary 1 0 1 0 1 1 0 1 Positional Values x x x xx x x x 2020 21212 2323 2424 2525 2626 2727 128 + 32 + 8 + 4 + 1 Products 173 10

14. 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

15. Decimal to Hexadecimal Conversion Convert 830 10 to its hexadecimal equivalent: 830 / 16 = 51 R14 51 / 16 = 3 R3 3 / 16 = 0 R3 33E 16 = E in Hex

16. Hexadecimal to Decimal Conversion Convert 3B4F16 to its decimal equivalent: Hex Digits 3 B 4 F xx x 16 3 16 2 16 1 16 0 12288 +2816 + 64 +15 15,183 10 Positional Values Products x

17. 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

18. Convert 010101101010111001101010 2 to hex using the 4-bit substitution code : 0101 0110 1010 1110 0110 1010 Substitution Code 5 6 A E 6 A 56AE6A 16