SUBJECT: COMPUTER DIGITAL DESIGN
Question:?One of the current dongles (modem) that the MTN mobile network provides has a maximum internet speed of 7.2 Mps. How many Kilobytes of data can you download in a minute using such an internet connection?
Answer all questions in this paper.
1. One of the current dongles (modem) that the MTN mobile network provides has a maximum
internet speed of 7.2 Mps. How many Kilobytes of data can you download in a minute using such
an internet connection? [10 Marks] 2. The MAC address of a WiFi network interface card is 00-1E-68-3F-73-E6. Convert this address
to binary. [10 Marks] 3. A newly created computer program detects the presence of Firefox, VLC and Logisim on any
computer it's installed. If none of the three is installed, the program won't run. The program
will ONLY run if either Firefox or VLC is running simultaneously with Logisim. The program
crushes if Firefox and VLC are running simultaneously.
(a) Construct a fully complete truth table depicting all the possible combinations and
outputs for the given requirements above. [5 Marks] (b) Construct the corresponding K-map from the truth table in (a). [5 Marks] (c) Derive and fully minimise the Boolean function from the K-map in (b). [5 Marks] (d) Draw a fully labeled digital circuit diagram of the minimised circuit. [5 Marks] 4. De Morgan?s theorem states that A + B = A ? B and it?s a theorem widely used in digital design.
(a) Prove the De Morgan?s theorem without using truth tables. [10 Marks] (b) Using the correct Boolean Identities, prove the Absorption Law as well as the
Distributive Law of Boolean Algebra. [10 Marks] 5. Compute the most positive and most negative 8-bit number that can be represented using;
a) Two?s complement number system [10 Marks] b) Sign/magnitude number system [10 Marks] 6. The XNOR (Exclusive NOR gate) is a digital logic gate whose function is the inverse of the
exclusive OR (XOR).
(a) Write down the truth table of the XNOR gate and deduce the corresponding Boolean
function using SoP. [10 Marks] (b) Sketch the circuit of an Exclusive NOR gate (XNOR) using basic logic gates, with inputs
A and B, and output F. [10 Marks] [100 Marks]