5 → is a symbol for an idea (the number 5)

312 → another symbol

300 + 10 + 2 = 312

we use base 10

 1   1   0   1
 x   x   x   x
2^3 2^2 2^1 2^0

8 +  4 + 0 + 1 = 13

• all info on comp is stored using 1s and 0s

112.625

binary numbers

• but positions in an n bit ninary number: 2^n-1 2^n-2 ...2^0
• ex: 1101

floating-point numbers

• the real number 1234.56 can be represented as 1.23456e3
• (1.23456 x 10 ^3)
• in scientific notation, the numbers are normalized so only one digit appears to the left of the decimal point
• -0.00099 is represented as -9.9e-4 (-9.9 x 10^4)

floating point notation

• sign-bit, exponent, mantissa (fractional part)

IEEE double-precision floating-point representation (64 bits)

• sign bit (first bit)
• exponent (next 11 bits) is 110