I have a small homework the teacher gave us to assess our previous Digital Logic course. The question is to design a combinational circuit whose input is a 5-bit binary number and whose output is the 2's complement of the input number. I am also told to use the Quine-McCluskey method to simplify the circuit.
I have started by constructing a truth table of 5 variables with possible 32 combinations.
--------------------------------
v w x y z A B C D E
--------------------------------
0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 1 1 1 1 1
.
.
1 0 0 0 1 0 1 1 1 1
.
.
1 1 1 1 1 0 0 0 0 1
--------------------------------
I have 5 outputs. I'm confused on how to procced with this.
Output A
can be expressed as:
A = v'w'x'y'z + v'w'x'yz' + v'w'x'yz + v'w'xy'z' + v'w'xy'z + v'w'xyz' +
v'w'xyz + v'wx'y'z' + v'wx'y'z + v'wx'yz' + v'wx'yz + v'wxy'z' +
v'wxy'z + v'wxyz' + v'wxyz + vw'x'y'z'
The same can be done for B
, C
, D
and E
. How do I proceed? Do I process (simplify) each output individually? If so, how can I combine them at the end?
Thanks,
Tamrat
Best Answer
As @oldfart suggested, instead of solving all those lengthy K-maps, you can directly draw the combinational ckt by using the relation that:
Two's compliment = One's compliment + 1
if input = \$A_4A_3A_2A_1A_0\$ and output = \$Z_5Z_4Z_3Z_2Z_1Z_0\$ , then:
\$Z_5Z_4Z_3Z_2Z_1Z_0\$ = \$A_4^1A_3^1A_2^1A_1^1A_0^1\$ + 00001
You can expand the Circuit further by substituting the equivalent gate level circuit of adders.