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Using only two-input NOR gates, show how AND, OR and NAND gates can be
made.
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The binary addition of two 2-bit 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, EX-OR and
inverter gates).
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If the 3-bit 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.
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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
two-input 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: Divide-by-N Counters
Doug Gingrich
Tue Jul 13 16:55:15 EDT 1999