1 The binary form can be used to represent all sorts of thin

#1

The binary form can be used to represent all sorts of things. For example, suppose five judges can vote either yes or no on an issue.

a. Find the minimum number of bits required to represent the collective vote, that is, to record all of the individual votes.

b. Repeat for the situation in which each judge can vote yes, no, or abstain.

#2

Repeat the entire last problem (both parts) under the constraint that each judge is assigned a separate binary field in the representation. That is, each judge’s vote is represented as a binary number, and then those 4 binary representations are concatenated (placed side-by-side) to form the representation of the collective vote.

Solution

1) a) As the five judges can vote yes or no so there are 2 possibilities. As there are 5 judges in total there are 32 (2^5 ) possibilities. So atleast 5 bits are required to represent this.

b) As now judges can also abstain. There are 3 possibilities. As there are 5 judges in total there are 243 (3^5 ) possibilities. So atleast 8 bits are required to represent this.

2) a) This won\'t change we can assign a single bit for each judge and 0 if votes no and 1 for yes.

b) This will change now for each judge we need to assign 2 bits. 00 for abstain, 01 for no and 10 for yes. So total we need 10(2*5) bits to represent the votes of all 5 judges.