3 Basic logic operations and symbols True only if all input conditions are trueANDORTrue only if one or more input conditions are trueNOTIndicates the opposite conditionXTrue/false conditions are represented by voltages:HIGH = true LOW = false
4 NOT gate also known as an inverter performs inversion or complementationHIGH ↔ LOW1 ↔ 0
5 NOT gate Truth TableAXA truth table shows the output corresponding to each possible inputThree equivalent ways to write the NOT condition:X = NOT AX = A’We’ll use truth tables extensively in the course
6 NOT gate Timing diagram A X A X Application: A group of inverters can be used to form the 1’s complement of a binary number:Binary number1’s complement
7 AND gateABXProduces a HIGH output when all inputs are HIGH; otherwise, the output is LOW
8 AND gate Truth table for a 2-input AND gate XTruth table for a 2-input AND gate0 00 11 01 11AND operation is sometimes shown with a dot between the variables, but it may be implied (no dot):AND operation is written as X = A·B or X = AB
9 AND gates have 2 or more inputs #inputs = n#input combinations (= #rows in truth table) = 2n2 inputs → 22 = 4 input combinations3 inputs → 23 = 8 input combinations4 inputs → 24 = 16 input combinationsWrite the truth table for a 3-input AND gate
20 Name the mystery gate #3Light turns on if this signal is LOW????Want green light ON if both tanks are at least 25% fullLevel sensor output is HIGH if tank is at least 25% full
21 XOR gate2-input exclusive-OR (XOR) gate produces a HIGH output if the inputs are at opposite logic levelsone HIGH & one LOWTruth table for a 2-input XOR gate0 00 11 01 11XOR operation is written3-input XOR defined:extends to N-input XOR
22 XNOR gateAXB2-input exclusive-NOR (XNOR) gate produces a HIGH output if the inputs are at same logic levelsboth HIGH, or both LOWTruth table for a 2-input XNOR gate0 00 11 01 11XNOR operation is written
24 1. The binary number 100011010100011011112 expressed in hexadecimal is: (a) AD46716(b) 8C46F16(c) 8D46F16(d) AE46F162. Convert the decimal number to hexadecimal
25 3. Express the decimal number 246910 in binary-coded decimal. 4. A communication system transmits 9-bit blocks of information using an even parity scheme. The following byte of information is to be transmitted:Calculate the value of the parity bit to be attached to this byte.
26 5. For the set of input waveforms shown below, draw the timing diagram showing the output X in relation to the inputs.
27 6. By examination of the timing diagram below, identify the type of 3-input gate which generates the output X.?
28 7. A 2-input gate with inputs A and B generates output X shown in the timing diagram below. The gate is:an OR gatean AND gatea NOR gatea NAND gateAXB
30 10. Compute the 2’s complement of 011011002 The decimal number is expressed in 8-bit 2’s complement form as:
31 12. Write −3410 as a binary number in 8-bit 2’s complement form 13. Convert each of the following decimal numbers to 8-bit 2’s complement form, and add them: −52 and 25.Check your answer by converting the result back to decimal.
32 14. Convert the hexadecimal number 6B16 to octal (base-8) 15. Perform the following addition of hexadecimal numbers:DF16 + AC16