04/18 Homework: Computer Number Systems and Boolean Algebra

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)

1 comment

Apr 25, 2021

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

AC + !(!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 law B!A + !B = !A + !B)

C + !A + !B (Absorption law AC + !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 law C!C = 0)

!A + !B + !C (Identity law + Absorption 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

Legion of Learners