| (a) | (i) A 1-bit full-adder has two
binary inputs A and B, a single binary outputs S (for sum) a carry-in, and a
carry-out. Copy and complete the following truth table for this component.
|
[2] |
| (ii) Draw and label a diagram to
show how full-adders can be combined to implement a 4-bit parallel adder. A block diagram
for a 4-bit parallel adder is shown below: Your implementation should have the same inputs and outputs as this block diagram.
|
[4] | |
| (iii) Draw and label a diagram to
show how exclusive-or gates can be added to make a 4-bit parallel adder into a
2's complement parallel adder/subtracter. Indicate clearly how the function of the circuit
may be switched between adding and subtracting. When substracting, the carry-out should be treated as a borrow-out: it should be at logic 1 if a borrow condition exists (if the magnitude of B3B2B1B0 is greater than that of A3A2A1A0).
|
[4] | |
| (b) | A binary-coded decimal (BCD) number
is a 4-bit binary number between 0000 and 1001. Two BCD numbers can be added by first
performing binary addition, and then adding 0110 if the result is greater than 1001 or
the binary addition results in a carry-out.
|
|
| (i) Draw and label a circuit diagram
to show how a single 4-bit parallel adder can be used to add 0110 to the binary number S3S2S1S0.
Label the BCD result T3T2T1T0, and remember to
set the carry-in to an appropriate value. You may ignore the carry-out. The addition of two BCD numbers results in a carry-out if and only if the correction - the addition of 0110 - is necessary.
|
[2] | |
| (ii) Draw and label a circuit diagram to show how two 4-bit parallel adders can be connected to produce a BCD adder. You may use and or or gates if necessary. The BCD adder should have two BCD inputs B3B2B1B0 and A3A2A1A0 and a single BCD output T3T2T1T0. You should also include a carry-in and a carry-out. | [8] |
