Bits, Bytes, Hex
Overview
Notes, study and understanding computer science fundamentals around bits, bytes and hex; how memory works, how to read and debug assembly.
Bits, Bytes, Hex
1 bit= 0 or 1 so "1 bit can represent 2 x numbers"1 byte= 8 bits i.e. 00000000, 00000001 and every combo of 8-bit 0's and 1's
| Numbers in 2 bits = 4 |
|---|
| 00 |
| 01 |
| 10 |
| 11 |
If we're calculating for 3 bits
Number in 3 bits | 2 * (No's in 2 bits) = 8 |
|---|---|
| 0XX | where XX is equal to the 2 bit calculation |
| 1XX | where XX is equal to the 2 bit calculation |
If we're calculating for 4 bits
Number in 4 bits | 2 * (No's in 3 bits) = 16 |
|---|---|
| 0XXX | where XXX is equal to the 3 bit calculation |
| 1XXX | where XXX is equal to the 3 bit calculation |
To summarize the sequence/pattern here:
- 1 bit = 2^1 = 2 numbers
- 2 bit = 2^2 = 4 numbers
- 3 bit = 2^3 = 8 numbers
- 4 bit = 2^4 = 16 numbers
N bits = 2^N numbers
How many numbers can
1 byterepresent?
N bits = 2^N numbers i.e. 2^8 = 256
binary to decimal
Take this binary number 10011101 and convert to decimal.
Read this as, "left most" position --> 10011101 <-- count positions starting from the "right most" position where the 1 is the "zero position", and moving to the left from there the 0 is the "first" position.
Position is counted starting from the right-most bit, and counting from 'zero'
Put the number veritcally into this table from the "left most" bit at top.
We ONLY do calculations on the 1 bits and skip the 0 bits.
| bit | calculation | result |
|---|---|---|
| 1 | 2^7 (7th position) | 128 |
| 0 | 6th position but 0 | 0 |
| 0 | 5th position but 0 | 0 |
| 1 | 2^4th position | 16 |
| 1 | 2^3 (3rd position) | 8 |
| 1 | 2^2 (3rd position) | 4 |
| 0 | 1st position but 0 | |
| 1 | 2^0 (zero position) | 1 |
The sum = 157 is the decimal representation of 10011101.
Hexadecimal
0...9A (10), B (11), C (12), D (13), E (14), F (15)
Take hex value 0x3EA
| bit | calculation | result |
|---|---|---|
| 3 | 3*16^2 (2nd position) | 3 x (256) = 768 |
| E | 14*16^1 (1st position) | 14 x (16) = 224 |
| A | 10*16^0 (zero position) | 10 x (1) = 10 |
The sum = 1002 is the decimal representation of 0x3EA