exam instructions_updated slides(1)[1]

exam instructions_updated slides(1)[1] - AnalogueVsDigital...

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10/13/2011 1 Week 12 Digital Logic Circuits Dr. Jayashri Ravishankar Room [email protected] [email protected] Analogue Vs Digital Original Signal Transmitted Signal (Modulated) Attenuated Signal Noise Received Signal Recovered Signal (Demodulated) Digital signal is less prone to accumulating noise, but it is not immune But the use of digital signal is in itself an error as the original signal is always analogue Analogue / Digital signals in telecommunication Data signal Modulated signal
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10/13/2011 2 Typical electronic systems Universal Voltage Encoding Why use digital? Good noise reject. High reliability Low drift High accuracy Predictable Low power Ease of design Limitations – generates noise – A/D & D/A interface costly Binary number system Has only two numerals, 0 and 1 Require very long strings of 1s and 0s The binary digits are also known as bits (11100110) 2 is an 8 bit number Nibble a group of four bits Byte a group of eight bits Word a group of sixteen bits; (Sometimes used to designate 32 bit or 64 bit)
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10/13/2011 3 (11100110) 2 = 0 x 2 0 + 1 x 2 1 +1 x 2 2 + 0 x 2 3 + 0 x 2 4 + 1 x 2 5 + 1 x 2 6 + 1 x 2 7 = 0 + 2 + 4 + 0 + 0 + 32 + 64 +128 = (230) 10 (101.101) 2 = 1 x 2 0 + 0 x 2 1 + 1 x 2 2 + (1 x 2 1 + 0 x 2 2 + 1 x 2 3 ) = 1 + 0 + 4 + (1/2 + 0 + 1/8) = (5.625) 10 Binary to decimal Decimal to Binary Binary addition 0 + 0 = 0 1 + 0 = 1 0 + 1 = 1 1 + 1 = 10 1 + 1 + 1 = 11 Example 1 1001001 + 11001 0 0 1 0 0 1 0 0 1 1 1 0 0 1 0 1 1 0 0 1 0 1 1 1 Check: (1001001) 2 = 1 x 2 0 + 1 x 2 3 + 1 x 2 6 = 1 + 8 + 64 = (73) 10 (11001) 2 = 1 x 2 0 + 1 x 2 3 + 1 x 2 4 = 1 + 8 + 16 = (25) 10 (1100010) 2 = 1 x 2 1 + 1 x 2 5 + 1 x 2 6 = 2 + 32 + 64 = (98) 10 73 + 25 = 98
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10/13/2011 4 Binary Subtraction Just like decimal numbers we can use borrow method for binary subtraction too. But we can't subtract a larger number from a smaller one column wise. For ex, consider 45 – 62 = 17. This cannot be done column wise. We need to identify the greater number. The computer method is to represent negative numbers in "two's complement" form. This allows us to directly subtract any pair of numbers, including greater from smaller and come up with the correct result. Binary Subtraction Usually MSB is allotted for representing sign. 0 is for + sign and 1 is for and sign. Ex, (5) 10 = (101) 2 (+ 5) 10 = (0101) 2 and ( 5) 10 = (1101) 2 (1101) 2 could be misinterpreted as (13) 10 We must first decide how many bits are going to be needed to represent the largest numbers we'll be dealing with, and then be sure not to exceed that bit field length in our arithmetic operations. Using 2’s complement A B becomes, A + ( B).
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