- Every time a character is typed on a keyboard a code number is transmitted to the computer.
- The code numbers are stored in binary on computers as Character Sets called ASCII.
- The table below shows a version of ASCII that uses 7 bits to code each character. The biggest number that can be held in 7-bits is 1111111 in binary (127 in decimal). Therefore 128 different characters can be represented in the ASCII character set (Using codes 0 to 127). More than enough to cover all of the characters on a standard English-Language keyboard.
- Click here for the full ASCII table.
- The ASCII has been used for a long time. But it has some
serious shortcomings:
- It only uses English alphabets.
- It is limited to 7-bits, so it can only represent 128 distinct characters.
- It is not usable for non-latin languages, such as Chinese.
- Character form of a decimal digit In ASCII, the number character is not the same as the actual number value. For example, the ASCII value 011 0100 will print the character '4', the binary value is actually equal to the decimal number 52. Therefore ASCII cannot be used for arithmetic.
* History of data encoding
As discussed last time, one of the fundamental requirements for a code set to be useful in WAN communications is that the sender and the receiver must agree on the meaning of each combination of ones and zeros. A 2-bit code set, for example, can have only four discrete meanings: one meaning each for the combinations 00, 01, 10, and 11. Go to three bits and you get eight codes; four bits yield 16, and five bits yield 32.
The first widely accepted code set was Baudot code, developed more than 100 years ago. By having five bits - and 32 code combinations - there were enough bit combinations available to have a unique code for each of the 26 letters of the alphabet.
However, 26 letters plus the 10 digits 0 through 9 exceed the 32 combinations. Rather than going to an additional bit, two unique codes are used to signal a shift between the "letters" interpretation of the code and the "figures" interpretation. Since both "letters" and "figures" tend to come in groups, this works fine for simple applications.
However, there's one big problem. With just five bits, there's no way to distinguish between UPPERCASE and lowercase letters. Going to a 6-bit code with 64 combinations would still be minimal, because it would take 62 combinations for the letters and digits, with only two codes left for punctuation.
Consequently, the minimal code set must consist of seven bits, and that's exactly what the American Standard Code for Information Interchange (ASCII) uses. This code, which has become the de facto standard for data communications, has 128 combinations, with a unique code for each letter in both uppercase and lowercase. In fact the binary code for each uppercase and lowercase letter is the same except for one bit, which is sometimes called the "shift" bit.
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1a. What is the minimum number of bits that are required to uniquely represent the characters of English alphabet? (Consider upper case characters alone)
The number of unique bit patterns using i bits is 2i We need at least 26 unique bit patterns. The cleanest approach is to compute log2 26 and take the ceiling .This yields 5 as the answer. Trial and error is also an acceptable solution.
1b. how many more characters can be uniquely represented without requiring additional bits?
With 5 bits, we can represent up to 32 (25) unique bit patterns; we can represent
32 - 26 = 6 more characters without requiring additional bits.
2 Using 7 bits to represent each number, write the representations of 23 and -23 in signed
Magnitude and 2's complement integers.
Signed Magnitude | 1's Complement | 2's Complement | |
23 | 0010111 | 0010111 | 0010111 |
-23 | 1010111 | 1101000 | 1101001 |
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