Computer Data Representation

Abstract

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• Provides standardised way to express measurements, allowing for easy comparison of values

Bit

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• Holds a value of 0 or 1

  
  

• Let n be the number of bits we have, where n>=1

• With n bits, we can represent $2^n$ values

$$2^n=2^{n-1}+2^{n-2}+\cdots +2^0$$

Given 2 bits

When n is $2$, 2^n = 4, 4 values: 00, 01, 10, 11 which are corresponding to 0,1,2,3.

Maximum value of n bits

Approach 1: $2^n-1$

Approach 2: $2^{n-1}+\dots +2^0$

Given 2 bit

n is $2$

• Approach 1: 2^2 - 1 = 3
• Approach 2: 2^1 + 2^0 = 3

How many bits are required to represent a decimal number?

Given $M$ is a decimal number, the number of bits required to represent it is the ceiling of log₂ M, which is represented with $\lceil {\log }_{2}M\rceil$.

Bit String

• A collection of 0s & 1s

Byte

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• A group of 8 Bit
• The smallest unit a programming language uses to store the data and instruction

KB vs KiB?

B refers to Byte, the K refers to $10^3$ and Ki refers to $2^{10}$. So 1KB is $1000$ bytes and 1KiB is $1024$ bytes.

Word

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• The size of a word can vary depending on the Instruction Set Architecture (ISA)
• A single unit of transfer from the Main Memory to the CPU and within the CPU
• Common word sizes are 16 bits, 32 bits, or 64 bits

How do we check if a given memory address is word-aligned?

It should divisible by the word size.

Qubit

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• Waiting to be explored