The numbers zero and one are so ubiquitous (present everywhere) in math and technology, that the question becomes, what are you doing with them?
In computer science, one and zero are the alphabet of the most primitive computer language, the language of off and on, or signal and no signal. This makes zero and one utterly fundamental to computer science.
In math, one is a unit, a very rare, very important type of number. Zero, representing nothing, also has special importance. Zero is linked to one by the successor function. Mathematicians tend to judge the importance of things by their usefulness, and zero and one are among the most used numbers in math, particularly in discrete math.
In logic, zero and one can be associated with the truth values: true and false. Zero and one are also the first two natural numbers, the natural numbers being important for establishing the idea of countability.
0 . . . . . 0 0 0 0 1 . . . . . 0 0 0 1 2 . . . . . 0 0 1 0 3 . . . . . 0 0 1 1 4 . . . . . 0 1 0 0 5 . . . . . 0 1 0 1 6 . . . . . 0 1 1 0 7 . . . . . 0 1 1 1 8 . . . . . 1 0 0 0 9 . . . . . 1 0 0 1 10 . . . . 1 0 1 0
| x | y | x' | y' | x⊕y | x'⊕y' | ---------------------------------- | 0 | 0 | 1 | 1 | 0 | 0 | | 0 | 1 | 1 | 0 | 1 | 1 | | 1 | 0 | 0 | 1 | 1 | 1 | | 1 | 1 | 0 | 0 | 0 | 0 |
Here they are for 1 to 16, at no extra cost:Dec . . . Bin1 . . . . . 12 . . . . . 1 03 . . . . . 1 14 . . . . . 1 0 05 . . . . . 1 0 16 . . . . . 1 1 07 . . . . . 1 1 18 . . . . . 1 0 0 09 . . . . . 1 0 0 110 . . . . 1 0 1 011 . . . . 1 0 1 112 . . . . 1 1 0 013 . . . . 1 1 0 114 . . . . 1 1 1 015 . . . . 1 1 1 116 . . . . 1 0 0 0 0
AnswerAnswer: ( 0! + 0! + 0! + 0! + 0! ) ! = 120 Explanation: Here we have used operator called " factorial ". As you know that 0! = 1 so, = ( 0! + 0! + 0! + 0! + 0! ) ! = ( 1 + 1 + 1 + 1 + 1 ) ! = (5 )! = 120 : ( 0! + 0! + 0! + 0! + 0! ) ! = 120 Explanation: Here we have used operator called " factorial ". As you know that 0! = 1 so, = ( 0! + 0! + 0! + 0! + 0! ) ! = ( 1 + 1 + 1 + 1 + 1 ) ! = (5 )! = 120
0-(-1) is the same as 0+1, so 0-(-1)=1
The Importance of Fibonacci's series is that it helps people find more patterns 1+0=1 1+1=2 1+2=3 2+3=5 5+3=8 etc.
Excess-3 BCD a B c d w x y z 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 1 0 0 1 0 0 1 1 0 0 0 1 1 0 1 1 1 0 1 0 0 1 0 0 0 0 1 0 1 1 0 0 1 0 1 1 0 1 0 1 0 0 1 1 1 1 0 1 0 1 0 0 0 1 0 0 0 1 0 0 1 i'm not sure. but it should be the ans
a b c y 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 FORMULA FOR possibilities = 2 ^(no of variables). Here its 4 so, 2n=24=16 Hence we have 16 possibilities.
w x y z 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 FORMULA FOR possibilities = 2 ^(no of variables). Here its 4 so, 2n=24=16 Hence we have 16 possibilities.
0 . . . 0 0 0 0 1 . . . 0 0 0 1 2 . . . 0 0 1 0 3 . . . 0 0 1 1 4 . . . 0 1 0 0 5 . . . 0 1 0 1 6 . . . 0 1 1 0 7 . . . 0 1 1 1 8 . . . 1 0 0 0 9 . . . 1 0 0 1 10 . . 1 0 1 0 11 . . 1 0 1 1 12 . . 1 1 0 0 13 . . 1 1 0 1 14 . . 1 1 1 0 15 . . 1 1 1 1 16. 1 0 0 0 0 . . etc.
11
0 . . . . . 0 0 0 0 1 . . . . . 0 0 0 1 2 . . . . . 0 0 1 0 3 . . . . . 0 0 1 1 4 . . . . . 0 1 0 0 5 . . . . . 0 1 0 1 6 . . . . . 0 1 1 0 7 . . . . . 0 1 1 1 8 . . . . . 1 0 0 0 9 . . . . . 1 0 0 1 10 . . . . 1 0 1 0
1 0 1 0 0 1 0 1 0 1 1 0 1 1 0 1 0 1 1 1 1 1 0 0 0 1 1 0 0 1
AND A B Q 0 0 0 0 1 0 1 0 0 1 1 1 OR A B Q 0 0 0 0 1 1 1 0 1 1 1 1 NOT A Q 0 1 1 0 (I might as well carry on) XOR A B Q 0 0 0 0 1 1 1 0 1 1 1 0 NAND A B Q 0 0 1 0 1 1 1 0 1 1 1 0 NOR A B Q 0 0 1 0 1 0 1 0 0 1 1 1 BUF (NNOT) A Q 0 0 1 1 XNOR A B Q 0 0 1 0 1 0 1 0 0 1 1 1
Strobe A B C D Output (Y) 0 0 0 0 0 D0 0 0 0 0 1 D1 0 0 0 1 0 D2 0 0 0 1 1 D3 0 0 1 0 0 D4 0 0 1 0 1 D5 0 0 1 1 0 D6 0 0 1 1 1 D7 0 1 0 0 0 D8 0 1 0 0 1 D9 0 1 0 1 0 D10 0 1 0 1 1 D11 0 1 1 0 0 D12 0 1 1 0 1 D13 0 1 1 1 0 D14 0 1 1 1 1 D15 1 X X X X 1 where A,B,C,D are the control input or control nibble and the Boolean expression for Y is given as:- Y = A'B'C'D'D0 + A'B'C'DD1 + A'B'CD' D2 + A'B'CDD3 + A'BC'D'D4 + A'BC'DD5+ A'BCD'D6 + A'BCDD7 + AB'C'D'D8 + AB'C'DD9 + AB'CD'D10 + AB'CDD11 + ABC'D'D12 + ABC'DD13 + ABCD'D14 + ABCDD15
1 - 0 - 0 - 1 = 0
| x | y | x' | y' | x⊕y | x'⊕y' | ---------------------------------- | 0 | 0 | 1 | 1 | 0 | 0 | | 0 | 1 | 1 | 0 | 1 | 1 | | 1 | 0 | 0 | 1 | 1 | 1 | | 1 | 1 | 0 | 0 | 0 | 0 |