Next: Data Acquisition and Process
Up: Digital Circuits
Previous: DividebyN Counters

Using only twoinput NOR gates, show how AND, OR and NAND gates can be
made.

The binary addition of two 2bit numbers (with carry bits) looks like
the following:
 Write a truth table expressing the outputs and as a
function of , and .
 Write an algebraic statement in Boolean algebra describing this
truth table.
 Implement this statement using standard (AND, OR, EXOR and
inverter gates).

If the 3bit binary number A B C represents the digits 0 to 7:
 Make a truth table for A, B, C and Q, where Q is true
only when an odd number of bits are true in the number.
 Write a statement in Boolean algebra for Q.
 Convert this equation to one that can be mechanized using only
two XOR gates. Draw the resulting circuit.

You need to provide a logic signal to control an experiment. The
experiment is controlled by the four signals A, B, C and D, which
make up the data word A B C D. The control line Q should be set
high only if this data word takes on the values 1, 3, 5, 7, 11 or 13.
 Write a truth table for this function.
 Using boolean algebra, write an expression indicating when Q
is true. Your statement should include one logical statement
for each of the six true conditions, each separated by the OR
function. Therefore this statement should utilize a number of
AND/NAND functions, and five OR statements.
 Simplify this statement so that it can be implemented using two
twoinput AND gates, one OR gate, one exclusive OR gate and one
logical inverter. The expression has the form
, where
stands for any of the four input signals or their logical
inverses.
 Implement this simplified function using logic gates.
Next: Data Acquisition and Process
Up: Digital Circuits
Previous: DividebyN Counters
Doug Gingrich
Tue Jul 13 16:55:15 EDT 1999