Computer number systems:

1. How many times does "010" appear in the binary representations of the octal numbers 12 to 71 inclusive? (leading 0s not included)

2. How many total 0s are in the binary representations of the hex numbers E to 20 inclusive?

3. How many 9-bit binary numbers are palindromes? (no leading 0s)

4. The number in brackets indicates the base. Complete the sequence:

10(10), 17(16), 100100(2), 61(8), ? (10)

Boolean Algebra:

5. Simplify: AC+!(B XOR A)+!B

6. Simplify: !(AB+ B XOR C) !C

7. Simplify: C XOR C

8. How many inputs are TRUE for the following expression: A(B XOR C)+!A!(B XOR C)

5.

AC + !(B XOR A) + !BAC + !(!BA + B!A) + !B(B XOR A = !BA + B!A)AC + B!A + !BA + !B(simplify!(!BA + B!A))AC + B!A + !B(Absorption law!BA + !B = !B)AC + !A + !B(Absorption lawB!A + !B = !A + !B)C + !A + !B(Absorption lawAC + !A = C + !A)6.

!(AB+ B XOR C) !C!AB + !(!BC + B!C) !C(B XOR C = !BC + B!C)!A + !B + B!C + !BC!C(DeMorgan's law + simplify!(!BC + B!C))!

A + !B + B!C + 0(Annihilator lawC!C = 0)!A + !B + !C(Identity law!B + B!C = !B + !C)7.

C XOR C!CC + C!C(C XOR C = !CC + C!C)0 + 0(Annihilator law + Annihilator law)0(Identity law)8. 4 inputs are true