# Falk Joensson'sLearning Programming with Eas(Easy Application Script Tutorial)

## How the Computer Works:04. To Bytes and Beyond

Each bit carries only a single yes-or-no information, such as "Is the A key pressed?". Most I/O devices, however, use signals that can have a wide range of values, like the brightness of a pixel on the monitor, or the movements of microphone and speaker membranes. Using a group of bits together, where each bit serves as a binary digit, you can create numbers to represent such signals. Using one bit: bit 0 = number 0 bit 1 = number 1 Using two bits: two bits 00 = number 0 two bits 01 = number 1 two bits 10 = number 2 two bits 11 = number 3 Using three bits: three bits 000 = number 0 three bits 001 = number 1 three bits 010 = number 2 three bits 011 = number 3 three bits 100 = number 4 three bits 101 = number 5 three bits 110 = number 6 three bits 111 = number 7 Each additional bit doubles the range of numbers. It repeats the prior range first completely with the leading bit set to 0, then again with the leading bit set to 1 and its 2^(n-1) value added. (100=4 is 000=0 + 4, 101=5 is 001=1 + 4, 110=6 is 010=2 + 4, 111=7 is 011=3 + 4.) With B as the number of bits, you can create B^2 different numbers: 1 bit: 0..1 (2 numbers) 2 bits: 0..3 (4 numbers) 3 bits: 0..7 (8 numbers) 4 bits: 0..15 (16 numbers) 5 bits: 0..31 (32 numbers) 6 bits: 0..63 (64 numbers) 7 bits: 0..127 (128 numbers) Early computers used 7 bits a lot, because this offers a range that is enough to represent a percentage value, and it also allowed for storing text files, which needs 26 letters both in lowercase and uppercase, 10 digits (together 2×26+10=62 characters) and several further characters such as space, . ! ? , ; : " - ( ), a line break and so on. Soon one further bit was added to create with 8 bits: 0..255 (256 numbers) the basic memory unit used by computers, named the byte, which can conveniently be written as a 2-digit hexadecimal number and has enough values (256) to cover many practical I/O and calculation needs. From then on, when more precise numbers or bigger numbers were needed, one did not add further bits, but rather used whole groups of bytes together. A group of two bytes was called a word (as 256×256 = 65,536, enough to cover even a very thorough dictionary of the English language), and two words (= more than 4 billion numbers!) was called a "double word". Various mathematical innovations allowed for Byte-based numbers being used optionally in a signed interpretation, for instance a signed byte does not represent 0..255 but -128..+127, and even in a scientific exponent notation, where floating-point numbers are written as m×10^x, with m and x being stored as signed bytes, words or double words in the computer.
04. To Bytes and Beyond
The passage describes how bits and bytes are used to represent information in computers, including the range of numbers that can be represented with different numbers of bits.
no_question
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Falk Joensson'sLearning Programming with Eas(Easy Application Script Tutorial)

## How the Computer Works:04. To Bytes and Beyond

Each bit carries only a single yes-or-no information, such as "Is the A key pressed?". Most I/O devices, however, use signals that can have a wide range of values, like the brightness of a pixel on the monitor, or the movements of microphone and speaker membranes. Using a group of bits together, where each bit serves as a binary digit, you can create numbers to represent such signals. Using one bit: bit 0 = number 0 bit 1 = number 1 Using two bits: two bits 00 = number 0 two bits 01 = number 1 two bits 10 = number 2 two bits 11 = number 3 Using three bits: three bits 000 = number 0 three bits 001 = number 1 three bits 010 = number 2 three bits 011 = number 3 three bits 100 = number 4 three bits 101 = number 5 three bits 110 = number 6 three bits 111 = number 7 Each additional bit doubles the range of numbers. It repeats the prior range first completely with the leading bit set to 0, then again with the leading bit set to 1 and its 2^(n-1) value added. (100=4 is 000=0 + 4, 101=5 is 001=1 + 4, 110=6 is 010=2 + 4, 111=7 is 011=3 + 4.) With B as the number of bits, you can create B^2 different numbers: 1 bit: 0..1 (2 numbers) 2 bits: 0..3 (4 numbers) 3 bits: 0..7 (8 numbers) 4 bits: 0..15 (16 numbers) 5 bits: 0..31 (32 numbers) 6 bits: 0..63 (64 numbers) 7 bits: 0..127 (128 numbers) Early computers used 7 bits a lot, because this offers a range that is enough to represent a percentage value, and it also allowed for storing text files, which needs 26 letters both in lowercase and uppercase, 10 digits (together 2×26+10=62 characters) and several further characters such as space, . ! ? , ; : " - ( ), a line break and so on. Soon one further bit was added to create with 8 bits: 0..255 (256 numbers) the basic memory unit used by computers, named the byte, which can conveniently be written as a 2-digit hexadecimal number and has enough values (256) to cover many practical I/O and calculation needs. From then on, when more precise numbers or bigger numbers were needed, one did not add further bits, but rather used whole groups of bytes together. A group of two bytes was called a word (as 256×256 = 65,536, enough to cover even a very thorough dictionary of the English language), and two words (= more than 4 billion numbers!) was called a "double word". Various mathematical innovations allowed for Byte-based numbers being used optionally in a signed interpretation, for instance a signed byte does not represent 0..255 but -128..+127, and even in a scientific exponent notation, where floating-point numbers are written as m×10^x, with m and x being stored as signed bytes, words or double words in the computer.
04. To Bytes and Beyond
user
The passage describes how bits and bytes are used to represent information in computers, including the range of numbers that can be represented with different numbers of bits.

TYPE: NO_QUESTION