Time Table Session 2021-22


 

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Introduction of K-Map (Karnaugh Map) Part 2

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  5 variable K-Map in Digital Logic Karnaugh Map  or K-Map is an alternative way to write truth table and is used for the simplification of Boolean Expressions. So far we are familiar with 3 variable K-Map & 4 variable K-Map. Now, let us discuss the 5-variable K-Map in detail. Any Boolean Expression or Function comprising of 5 variables can be solved using the 5 variable K-Map. Such a 5 variable K-Map must contain   = 32 cells . Let the 5-variable Boolean function be represented as : f ( P Q R S T)  where P, Q, R, S, T are the variables and P is the most significant bit variable and T is the least significant bit variable. The structure of such a K-Map for SOP expression is given below : The cell no. written corresponding to each cell can be understood from the example described here: Here for variable  P=0, we have Q = 0, R = 1, S = 1, T = 1 i.e. (PQRST)=(00111)  . In decimal form, this is equivalent to  7 . So, for the cell shown above the c...
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Alternate Logic-Gate Representations

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Alternate Logic-Gate Representations We have discussed the five basic logic gates (AND, OR, INVERTER, NAND, and NOR) and the standard symbols used to represent them in a logic circuit diagram. Most of the logic networks use standard symbols. But in some networks an alternative set of symbols is used in addition to the standard symbols. The table shows the alternate set of symbols for the five basic gates. Table: Alternate Logic Gate Representations To convert any normal symbol to its corresponding alternate symbol, the following steps are used: METHODOLOGY: TO CONVERT STANDARD SYMBOL TO ALTERNATE SYMBOL Step 1: Add bubbles (indication of inversion) at those input or output points where it is not present. Step 2: Remove all pre-existing bubbles of the normal symbol, if there is any at the point (only NOT, NAND and NOR gates) Step 3: If the existing normal logic symbol is AND, change it to OR, Similarly, if it is OR, then change it to AND. There is no change for the triangular symbol of ...
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Number Systems

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  Table: - Various number systems and their bases S. No Name of Number System Base/Radix 1. Binary 2 2. Octal 8 3. Decimal 10 4. Hexadecimal 16 Table: - number systems S. No Name of Number System Base/Radix First Digit Last Digit All Digits/ Characters 1. Binary 2 0 1 0,1 2. Octal 8 0 7 0,1,2,3,4,5,6,7 3. Decimal 10 0 9 0,1,2,3,4,5,6,7,8,9 4. Hexadecimal 16 0 F 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F Table: - Number Formats S. No Name Size (bits) Example 1. Bit 1 1 2. Nibble 4 1010 3. Byte 8 1000 1100 4. Word 16 1010 1010 1010 1010 5. Double Word 32 1100 1100 1100 1100 1100 1100 1100 1100 Table: - Decimal, Binary, Octal and Hexadecimal Number S. No Decimal Binary Octal Hexadecimal 1. 0 0000 0 0 2. 1 0001 1 1 3. 2 0010 2 2 4. 3 0011 3 3 5. 4 0100 4 4 6. 5 0101 5 5 7. 6 0110 6 6 8. 7 0111 7 7 9. 8 1000 10 8 10. 9 1001 11 9 11. 10 1010 12 A 12. 11 1011 13 B 13. 12 1100 14 C 14. 13 1101 15 D 15. 14 1110 16 E 16. 15 1111 17 F 17. 16 0001 0000 20 10 18. 17 0001 0001 21 11 19. 18 0001 0010 22 12 ...
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