One way to code decimal expansions using bits is to use the four bits of the bin

Question

One way to code decimal expansions using bits is to use the four bits of the binary expansion of each digit in the decimal expansion. E.g. 873 is encoded as 100001110011. This encoding of a decimal expansion is called a binary coded decimal expansion. or BCD. Since there are 16 ways to write 4 bits numbers, and only 10 decimal digits, there are 6 combinations of 4 bits that arc not used to encode digits. Suppose that a circuit is to be built that produces an output of 1 if the decimal digit is 5 or greater, and an output of 0 if the decimal digit is less than 5. How can this circuit be built using only AND, OR. and NOT gates? Construct the simplest circuit possible.

Explanation / Answer

ther are two questions. what to explain F(w,x,y,z)'= ((xyz')(y'z+x)' + (w'yz+x'))' = ((xyz')(y'z+x)')' (w'yz+x')' = ((xyz')' + (y'z+x)) ((w'yz)'x = ((x'+y'+z) +(y'z+x)) ((w+y'+z')x = (x'+y'+z+y'z+x) (wx+xy'+xz') = (x'+x'+y'+y'z+z) ( = (x'+y'+z) (x(w+y'+z') = (xy'+xz) (w+y'+z') = (x'+y+x'+z) (w'yz) = (x'+y+z) (w'yz) = (xy'z'+wy'z') = (x+w)(y'z') = (x'w'+y+z) is the final answer.

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