Question

1-22 The (r — l)’s complement of base-6 numbers is called the 5’s complement.
(a) Determine a procedure for obtaining the 5’s complement of base-6 numbers.
(b) Obtain the 5’s complement of (543210)6 -
(c) Design a 3-bit code to represent each of the six digits of the base-6 number system. Make the
binary code self-complementing so that the 5’s complement is obtained by changing 1 ’s to
0’s and 0’s to l’s in all the bits of the coded number.

Answer 1

Explanation:

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Answer 2

Answer:

a) Procedure for obtaining the 5’s complement of base-6 numbers.

• Firstly, subtract 5's from the given number.
• Then add 1 to the resultant.
• This will give us the 5's complement of base-6 number.

(b) Obtain the 5’s complement of (543210)₆

• Subtracting the same number of 5's from the given number,

555555 - 543210 = 12345

• Now adding 1 to it.

12345 + 1 = 12346

We get, (12346)₅

This is our 5's complement.

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