Tuesday, April 23, 2013

tips and tricks for digital number formats, logic gates and Boolean Algebra.

from one of my colleagues - thanks Anon.
  • You must be really comfortable in interchanging between types of number representation.
  • Write down the RANGE for every number representation available in your notes.
  • A XOR B = ~AB + ~BA
  • De Morgan’s rule, De Morgan’s rule everywhere. Not only on Boolean algebra, some ALU questions have them.
  • If there seems to be no answer, try using De Morgan’s rule if appropriate.
  • From my experience, (tutors please correct me if I am wrong), using De Morgan’s rule on 3 variable also works.
  • BOOLEAN IDENTITIES, the easiest and most important including:
AA = A, A + A = A, (A+ BC) = (A+ B)(A+C), A(A+B) = A, A + AB = A

Knowing this only is not enough, you NEED practice. For those of you who are going to say “challenge accepted”, go on, make my day.

  • How to convert from one’s complement to two’s complement? add the sign to the number. e.g. 1110 in one’s complement: add the sign to the number, 1110 + 1 = 1111 in two’s complement. second example, 0110 in one’s complement: add the sign to the number, 0110 + 0 = 0110 in two’s complement.
  • Conversely, from two’s complement to one’s complement, take the sign number instead of adding.
  • Negative numbers also have odd and even.
  • Two’s complement, signed number, unsigned, excess-128: don’t affect whether it is odd or even.
  • One’s complement however, when negative: the LSB is 1 for even, 0 for odd. When positive à 0 for even, 1 for odd.
  • Binary Coded Decimal: e.g. 789, become 0111 1000 1001. Always use 4 bits for each number (since max is 9, 1001).
  • I wasted a lot of time simplifying the sum of products on questions 53 – 57 on sample midsem paper. IMO it is quicker to just sub in A B C with their value on the table and see if the result matches.
  • Use ruler for questions like q110.
  • 2 inputs XOR gate and NAND gate can be used as an inverter. If one input is 1 and is fixed, no matter what the other input is, the output will be that other input inverted. e.g. 1 XOR A = ~A. 1 NAND A = ~A.

Friday, April 5, 2013

Designing circuits in logisim...

Logisim is great to prototype your circuits. This one worked, thankfully - as I also designed it on paper a couple of times which took a while :D

If any 2 of 3 bits of input in an incoming bitstream (B) are 1's then X will be 1,
(the X output LED will light up)
and if 3 1's re detected - the Y output will be 1
(the Y LED will light up)

You can 'poke' the clock to make it tick over after you've adjusted your inputs, or you can mke it tick automatically at a given Hz.  

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