| (a) | Calculate the value of the expression
and give the result in base 8.
|
[4] |
| (b) | The following circuit shows a controller for a
lightbulb using four switches and a battery.
Give a boolean expression describing the state of the lightbulb, in terms of the settings of the switches W, X, Y, Z. Use 1 for a closed (conducting) switch and 0 for an open switch, and 1 for the lightbulb being on and 0 for it being off.
|
[2] |
| (c) | Express the following circuit symbolically.
Redraw the circuit using a single gate, and express the new circuit symbolically too.
|
[3] |
| (d) | By constructing a Karnaugh map, find a minimal
product-of-sums expression for the function F (A, B,
C, D) =
|
[3] |
| (e) | Complete the diagram below so that the device
can act as a 4-bit adder/ subtractor with A/S' as the switch. ( Each full adder
FA has inputs bits A and B and carry in Ci, and output bit S
and carry out Co. The switch A/S' selects addition if it is high, and
subtraction if it is low.) Show all the relevant components and connections to and within
the dotted box.
|
[6] |
| (f) | Give the truth-table for a 1-to-8
demultiplexor, with a data input A, three selector inputs S0 to S2,
and eight data outputs B0 to B7.
|
[2] |
(2, 4, 5, 6, 7, 10, 12, 13, 14, 15)