Basics of digital electronics
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The document discusses different number systems used in computers such as binary, decimal, hexadecimal, and octal. It explains how computers use binary digits for operations and how different number systems are converted between each other. For example, binary numbers are converted to decimal by multiplying each bit by its place value and summing the results. Negative numbers are represented using ones' complement and twos' complement in binary. Basic logic gates and flip-flops used in digital circuits are also introduced.
Basics of digital electronics
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- 2. 2 2 +1 =3 HOW THE COMPUTER GETS THE ANSWER
- 3. 3 A computer understands information composed of only zeros and ones. The decimal number system is convenient for the programmer. The computer uses binary digits for its operation. 0 1 0 1 1 0 1 1 0 0 1 0
- 5. DECIMAL NUMBER SYSTEM 5 • 0,1,2,3,4,5,6,7,8,9.DIGITS • 10BASE
- 13. 13 CONVERSIONS IN BASIC NUMBER SYSTEM
- 14. 14 BINARY TO DECIMAL • 1 0 1 0 1 BINARY • 5 4 3 2 1 BIT POSITION • 1*2 +0*2 +1*2 +0*2 +1*2. MUL WITH BASE • 21 DECIMAL4 3 2 1 0
- 15. 15 HEXADECIMAL TO DECIMAL •5A9 HEX •3 2 1 BIT POSITION • 5*16 +A*16 +9*16 MUL WITH BASE •1449 DECIMAL2 1 0
- 16. 16 OCTAL TO DECIMAL •645 OCTAL •3 2 1 BIT POSITION •6*8 +4*8 +5*8. MUL WITH BASE •421 DECIMAL 2 1 0
- 17. 17 DECIMAL TO BINARY • Q=19 • R=139 • Q=9 • R=119 • Q=4 • R=19 • Q=2 • R=04 • Q=1 • R=02 • Q=0 • R=11 LSB MSB Divide through out by 2 DECIMAL = 39 BINARY = 100111
- 18. 18 DECIMAL TO HEX • Q=2 • R=335 • Q=0 • R=22 Divide through out by 16 LSB MSB DECIMAL = 35 HEX = 23
- 19. 19 DECIMAL TO OCTAL • Q=57 • R=5461 • Q=7 • R=157 • Q=0 • R=77 Divide through out by 8 LSB MSB DECIMAL = 461 OCTAL = 715
- 20. 20 BINARY TO HEXADECIMAL BINARY • (010111011001) 4BITS DIV • (0101)(1101)(1001) HEX • (5) (D) (9) =(5D9)2 16
- 21. 21 BINARY TO OCTAL BINARY • (101111100) 3BIT DIV • (101)(111)(100) OCTAL • (5) (7) (4) =(574) 2 8
- 22. 22 HEXADECIMAL TO BINARY HEX • (5C) EXPANSION • (0101)(1100) BINARY • (01011100)16 2
- 23. 23 OCTAL TO BINARY OCTAL • (436) EXPANSION • (100)(011) BINARY • (100011) 8 2
- 24. 24 HEXADECIMAL TO OCTAL • (4DF)HEX • (0100)(1101)(1111)EXP • (010011010000)BINARY • (010)(011)(011)(111)3BIT DIV • (2337)OCTAL 16 2 8
- 25. 25 OCTAL TO HEXADECIMAL • (456)OCTAL • (100)(101)(110)EXP • (100101110)BINARY • (0001)(0010)(1110)4BIT DIV • (12E)HEX 8 2 16
- 26. 26 REPRESENTATION OF NEGATIVE NUMBER 9’S & 10’S COMPLIMENT • DECIMAL NUMBER SYSTEM 1’S & 2’S COMPLIMENT • BINARY NUMBER SYSTEM
- 27. 27 BINARY ARITHMETIC 1 • BINARY ADDITION 2 • BINARY SUBTRACTION 3 • BINARY MULTIPLICATION 4 • BINARY DIVISION
- 28. 28 0 + 0 = 0 1 + 0 = 1 0 + 1 = 1 1 + 1 = 0 1 (Carry bit) BINARYADDITION 1 1 0 1 (13 decimal) +0 0 0 1 (+1 decimal) 1 1 1 0 (14 decimal)
- 29. 29 BINARY SUBTRACTION 0 ‐ 0 = 0 1 ‐ 0 = 1 0 ‐ 1 = 1 1 (Carry bit) 1 ‐ 1 = 0 1 1 0 1 (13 decimal) + 0 0 1 1 (-3 decimal) 1 0 1 0 (10 decimal) Borrow
- 30. 30 1 0 0 0 =810 X 0 1 1 0 =610 0 0 0 0 + 1 0 0 0 + 1 0 0 0 + 0 0 0 0 0 1 1 0 0 0 0 = 4810 BINARY MULTIPLICATION
- 31. 31 BINARY DIVISION 011 ) 0 1 1 0 0 1 0 ( 1 0 1 1 0 0 0 (0 0 0 0 0 0 0 (0 0 0 0 0 0 1 (0 0 0 0 0 1 0 Q=1000=1610 R=10= 210
- 32. 32 SIGNED ARITHMETIC OPERATION MSB bit is reserved to represent the sign of the number. When the number is negative, the sign bit is kept one. When the number is positive, the sign bit is 0. In 8-bit processor, MSB = sign bit & other 7 bits = number. In 16-bit processor, MSB = sign bit & other 15 bits = number.
- 33. 33 EXAMPLES 0 0 0 0 0 1 0 1 (+5 decimal) 0 0 0 0 0 1 0 0 (+4 decimal) 0 0 0 0 1 0 0 1 (+9 decimal) 0 0 0 0 0 1 0 1 (+5 decimal) 1 0 0 0 0 0 1 0 (-2 decimal) 1 1 1 1 1 1 0 1 (1’comp of -2) 1 1 1 1 1 1 1 0 (2’s comp of -2) 0 0 0 0 0 0 1 1 (+3 decimal) 1 2 1 2 1
- 34. 34 BCD AND GRAY CODE
- 35. 35 LOGIC GATES Logic gates perform basic logical functions. They are fundamental building blocks of digital integrated circuits. Most logic gates take an input of two binary values, and output a single value of a 1 or 0. Some circuits may have only a few logic gates, while others, such as microprocessors, may have millions of them. There are seven different types of logic gates, which are outlined.
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- 43. 43 FLIP-FLOPS A flip-flop or latch is a circuit that has two stable states and can be used to store state information. Each flip-flop stores one bit of information
- 44. 44 THANK YOU