Numbering and coding systems
􀂉 Digital primer
􀂉 Inside the computer

Human beings use base 10 (decimal)
arithmetic
􀂾 There are 10 distinct symbols, 0, 1, 2, …,
9
􀂉 Computers use base 2 (binary) system
􀂾 There are only 0 and 1
􀂾 These two binary digits are commonly
referred to as bits

􀂉 Divide the decimal number by 2
repeatedly
􀂉 Keep track of the remainders
􀂉 Continue this process until the quotient
becomes zero
􀂉 Write the remainders in reverse order
to obtain the binary number
Ex. Convert 2510 to binary
Quotient Remainder
25/2 = 12 1 LSB (least significant bit)
12/2 = 6 0
6/2 = 3 0
3/2 = 1 1
1/2 = 0 1 MSB (most significant bit)
Therefore 2510 = 110012