Computers store all numbers in binary format using a base-2 system of 0s and 1s to represent the on and off states of transistors. There are different types of numbers that can be stored, including integers which can be unsigned or signed at the cost of one bit of precision for the sign, and floating point numbers which are optimized for fractional values using scientific notation format with sections for the sign, exponent, and mantissa/significant digits. Floating point numbers specifically have single precision floats stored in 1 bit for the sign, 8 bits for the exponent, and 23 bits for the mantissa, while double precision doubles are stored with 1 bit for the sign, 11 bits for the exponent, and 52 bits for the mant

1. Numbers

2. Types of numbers

3. Binary
• Computers store all numbers in base 2
• Base 2 equates to on and off state of transistors
• This is a current physical constraint of computers.
• Computers convert numbers to base 10, 8, and 16 for our
benefit.

4. Integers
• Integers come in two varieties (unsigned and signed)
• Signed integers lose one bit of precision to store sign.

5. Floating Point Numbers
• Built to deal with fractional numbers
• Really fast
• Basically scientific notation

6. How they’re stored
Sign Exponent Mantissa / Significant

7. Floats vs Doubles
Sign Exponent Mantissa / Significant
1bit 8 bits 23bits
Doubles: 1 / 11 / 52