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Showing posts from January, 2011

### Canonical Forms and Standard Forms

Standard Formseach term in the function can have any number of literals.Example, F1 = a +b’c + cde There are 5 variables in F1 (a,b,c,d,e)Canonical form terms should be written as m0, m1… (sum of Products) or M0, M1, M2… (Product of sums). Each term in the canonical form should have all the literals. Example: F1 = ab’c’d’e’ + abcd’e’ + abcdeMore about Canonical FormsMintermsIt is Sum of Products Canonical form is Sum of Mintermsthree variable minterms are shown belowxabcminterms0000m0=a’.b’.c’1001m1=a’.b’.c2010m2=a’.b.c’3011m3=a’.b.c4100m4=a.b’.c’5101m5=a.b’.c6110m6=a.b.c’7111m7=a.b.cMaxtermsProduct of Sum (PoS)Canonical form is Product of MaxTermsthree variable maxterms are shown belowxabcminterms0000M0=(a+b+c)1001M1=(a+b+c’)2010M2=(a+b’+c)3011M3=(a+b’+c’)4100M4=(a’+b+c)5101M5=(a’+b+c’)6110M6=(a’+b’+c)7111M7=(a’+b’+c’)usually Mi = (mj)’Express the boolean function F = A + BC in a sum of minterms. The function has three variables, so F = A + BC will be F = A(B + B’) + (A +A’) BC  [sin…

### Binary Codes

bit is just called as binary digitTo represent 2n elements, n bits are neededHere are the following Binary Codes, For example, the BCD code is otherwise called as 8421 code where the 8,4,2,1 are the weights assigned to the digitsfor number 3 (0011), the weightage will be 0 * 8 + 0 * 4 + 1 * 2 + 1 *1in 84-2-1 code, the weights are arranged like this, for example, for number 2 (0110),  it is 0 * 8 + 1 * 4 + 1 * –2 + 0 * –1similarly the same case for 2421 codes.Excess – 3 is a code which is in excess of 3 in decimal numbers .Error Detection CodesBinary information is usually transmitted from one place to other through wired medium, due to the electromagnetic radiation or external noise, the information bits can be changed (ie 1 to 0 or 0 to 1), in this scenario, there is a provision to check whether the given word or byte is correct or not. Parity bits are used for that.Odd parity or even parity is adopted based on the application, but mostly even parity is adopted.Parity bit is an extra…