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Question: Design and implement a 3 bit binary to excess 3 code converter using CMOS transistors(input three bit, output four
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An excess 3 code, as can be predicted from its name, is an excess of three of the binary number. Simply add three to binary number and represent that in binary form, that will be your excess 3/xs3 code.So, 0000 in binary will be equivalent to (0+3=3) 0011 in excess 3.

Yes, the number is written in binary format and that can be a source of confusion. Think of it this way, you have a normal number system, however, your friend wants to be unique and says that for him a six will equal to your three. The representation is same however, the values differ by three.

B2 B1 B0 E2 E1 E0
0 0 0 0 0 1
0 0 1 1 0 1
0 1 0 1 0 1
0 1 1 1 1 0
1 0 0 1 1 1
1 0 1 × × ×
1 1 0 × × ×
1 1 1 × × ×

Lets obtain the equation for the code converter circuit using K-maps

E2 = B0 + B1 + B1'B2 OR E2 = B0+B1+B2 (if you take cells 4,5,6,7)(both are correct)

E1 = B2 +

E0 = B0'

Hnece, from the equations above we can design the following combinational logic circuit for 3-bit binary to excess 3 code converter circuit

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