# Bits & Bytes

Simple definition of Bits & Bytes
Bit
• a "bit" is atomic: the smallest unit of storage
• A bit stores just a 0 or 1
• "In the computer it's all 0's and 1's" ... bits
• Anything with two separate states can store 1 bit
• In a chip: electric charge = 0/1
• In a hard drive: spots of North/South magnetism = 0/1
• A bit is too small to be much use
• Group 8 bits together to make 1 byte
Byte
• One byte = collection of 8 bits
• e.g. 0 1 0 1 1 0 1 0
• One byte can store one character, e.g. 'A' or 'x' or '\$'
One Byte - 256 Patterns
• 1 byte is group of 8 bits
• 8 bits can make 256 different patterns
• How to use the 256 patterns?
• How to store a number in a byte?
• Start with 0, go up, one pattern per number, until run out of patterns
• 0, 1, 2, 3, 4, 5, ... 254, 255
• One byte can hold a number between 0 and 255
• i.e. with 256 different patterns, we can store a number in the range 0..255
• Really good for storing characters/letters.
Bit Notation
• A single bit is only ever a zero or a one — it has only two possible states[0,1]For two bits we get a total of four possibilities: [00, 01, 10, 11].
• Following this pattern, it becomes fairly obvious that for every n bits we have 2^n possible states.
• Eventually, the need for more symbols & letters, in order to make working with computers more developer-friendly, came to the forefront of computer scientists gaze: how does one build a number system, let alone an entire alphabet, from only 0s & 1s?
Bytes and Beyond
• We’ve now covered the birth & pragmatism of computing with, as well as defining, bits. From there we explained how four bits (2⁴) give us our hexadecimal system & how eight bits (2⁸) give us our still-in-use extended ASCII language. We’re now going to introduce a final principle that’ll hopefully make it clear why understanding the fundamentals of bits is crucial to a thorough understanding of cryptography & by extension cryptocurrencies.
• Eight bits (2⁸) is actually a super important number in not just cryptography & cryptocurrencies but in all computing. In fact, eight bits are so standard that they were given a new name to symbolize an eight-bit string: a byte. byte is a string of eight bits: 8 bits = 1 byte.
• The fact that bytes can represent a single character is a key reason why factors of eight are extremely common numbers in cryptography, such as 128, & 256 (from the famous Bitcoin consensus hashing algorithm SHA256). Intuitively understanding how to go from bits, to hexadecimal values to alphanumeric characters to bytes is going to be a core part of needed knowledge moving forward to really understanding the driving forces behind cryptocurrencies.
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