S -> APY | AQZ
A -> D { D }
D -> P | Q
P -> '1' | '3' | '5' | '7' | '9'
Q -> Y | Z
Y -> '2' | '6'
Z -> '0' | '4' | '8'
What is a simple characterization for the strings this grammar generates?
2. Construct a grammar that generates all
legal rex lists that contain single-digit leaves. Nested lists should
be permitted, but the grammar should
not generate other strings. Do not worry about whitespace (assume none).
Examples of lists your grammar should generate include Consider the 7-segment
"decoder": Seven segment LED display
Display of 0 through 9 with a
seven segment display 3. In the following, assume that any digit (0-9)
is to be displayed on a 7-segment display. Consider the function
that has as input the binary representation of that digit (0-9) and
as output, the state of the segments of the seven-segment display. (Lit
is 1, unlit is 0.) Create
a truth table for this switching function that maps four bits to seven bits.
4. Give a Karnaugh map (with don't cares) for
each of the switching functions. Write the simplified sum-of-products
form of each, taking advantage of "don't cares." 5. Construct a logic circuit which computes the state of
the last segment (s6) in the seven-segment display, given the four bits
of input.
[]
[1]
[1,5,7,0]
[1,[2,3],4,[[5]]]
s0: s1:
s2: s3:
s4: s5:
s6:
