1. Convert the following binary numbers in decimal: 101110; 1110101; and 110110100.
2. Convert the following decimal numbers to the bases indicated.
a. 7562 to octal
b. 1938 to hexadecimal
c. 175 to binary
3. Show the value of all bits of a 12-bit register that hold the number equivalent to decimal 215 in (a) binary; (b) octal; (c) hexadecimal; (d) binary-coded decimal (BCD).
4. Determine by means of a truth table the validity of DeMorgan's theorem for three variables: (ABC)' = A' + B' + C'.
5. Simplify the following expressions using Boolean algebra.
a. AB + A(CD + CD')
b. (BC' + A'D) (AB' + CD')
6. Given the Boolean expression F = x'y + xyz':
a. Derive an algebraic expression for the complement F'.
b. Show that F·F' = 0.
7. Simplify the following Boolean functions, using 3-variable maps:
a. F (x,y,z) = Σ(0,2,6,7)
b. F(A,B,C) = Σ (0,2,3,4,6)
8. Simplify the following Boolean functions, using 4-variable maps:
a. w'z + xz + x'y + wx'z
b. wxy + yz + xy'z + x'y