Overview
This lecture introduces the fundamentals of binary and decimal conversions, focusing on their importance in IP subnetting and practical calculations.
Binary Number System Basics
- Binary uses only two digits: 0 and 1.
- Each binary digit is called a "bit."
- Eight bits together make a "byte" or "octet" (8-bits).
Binary to Decimal Conversion
- Create a conversion chart with powers of two: 1, 2, 4, 8, 16, 32, 64, 128 (for 8 bits).
- Align the binary number with the conversion chart from right to left.
- For every binary '1', add the corresponding chart value; for '0', add nothing.
- Example: 00000010 in binary = 2 in decimal.
- Example: 10000010 in binary = 128 + 2 = 130 in decimal.
- Example: 11111111 in binary = 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255 in decimal.
Decimal to Binary Conversion
- Use the conversion chart and start with the highest value less than or equal to the decimal number.
- Place a '1' where the chart value fits and subtract; '0' where it doesn't.
- Example: 154 decimal = 10011010 in binary.
- Process: Check each power of two in order, filling in bits with 1 or 0.
Calculating Possible Values with Bits
- Number of possible values with n bits is 2^n.
- 2 bits: 4 outcomes (00, 01, 10, 11) = 0, 1, 2, 3 decimal.
- 3 bits: 8 outcomes; 4 bits: 16; 5 bits: 32; 6 bits: 64; 7 bits: 128; etc.
- Each increase in bit count doubles the number of possible values.
Key Terms & Definitions
- Bit — a single binary digit, 0 or 1.
- Byte/Octet — a group of 8 bits.
- Binary — a base-2 numbering system using only 0 and 1.
- Decimal — a base-10 numbering system using digits 0–9.
- Conversion Chart — a table of powers of 2 used to convert binary to decimal and vice versa.
Action Items / Next Steps
- Practice converting numbers between binary and decimal using the conversion chart.
- Prepare for the next section on IP subnetting using these binary conversion skills.