1. Other characters besides numbers can be represented in binary. For example, h
ID: 2080473 • Letter: 1
Question
1. Other characters besides numbers can be represented in binary. For example, how many bits are required for a binary representation of:
a. The 26 upper-case letters in the English alphabet?
b. All of the upper-case and lower-case letters in the English alphabet?
c. All of the upper-case and lower-case letters in the English alphabet, the 10 numerals, and 15 punctuation marks?
2. The binary form can be used to represent all sorts of things. For example, suppose four 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
Explanation / Answer
1.a. The number of unique bit patterns using i bits is 2 to the power of i. We need at least 26 unique bit patterns. The cleanest approach is to compute log2 26 and take the ceiling (round up). This yields 5 as the answer. Trial and error is also an acceptable solution.
1.b. The number of unique bit patterns using i bits is 2 to the power of i. We need at least 52 unique bit patterns. The cleanest approach is to compute log2 52 and take the ceiling (round up). This yields 5.700 as the answer which can be approximated as 6.
1.c.The number of unique bit patterns using i bits is 2 to the power of i. We need at least 26+26+10+15=77
patterns. The cleanest approach is to compute log2 77nd take the ceiling (round up). This yields 6.2687 as the answer which can be approximated as 7
2.a. 4judges can cast 4votes that means 2 bits of binary digits are sufficient in the way that have only one choice either to cast yes or no as their vote.
2.b. In case of choice of yes or no votes for 4 judges 3 bit pattern is required
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