Digital Logic Design and
Computer Architecture
Dr. Rahma Bouaziz, maître-assistant, FSG
A.U. 2023_2024
Chapter 2 – Part 1
Numbering system and
coding
Digital Computer Systems
● Digital systems consider discrete amounts of data
● Examples
● 26 letters in the alphabet
● 10 decimal digits
● Larger quantities can be built from discrete values:
● Words made of letters
● Numbers made of decimal digits (e.g. 239875.32)
9/28/2023 3
, In the Beginning
• In the beginning people represented numbers
base 10 because we have ten fingers.
9/28/2023 4
Understanding Decimal Numbers
● Decimal numbers are made of decimal digits:
(0,1,2,3,4,5,6,7,8,9) Base = 10
● But how many items does a decimal number
represent?
● 8653 = 8 x103 + 6 x102 + 5 x101 + 3 x100
● Number = d3 x B3 + d2 x B2 + d1 x B1 + d0 x B0 = Value
● What about fractions?
● 97654.35 = 9x104 + 7x103 + 6x102 + 5x101 + 4x100 + 3x10-1 + 5x10-2
● In formal notation → (97654.35)10
9/28/2023 5
Ways to "represent" a number…
• There are many ways to "represent" a number
ignored in life but important for computers.
• Representation does not affect the result of an
operation but representation affects difficulty of
computing result
• For computer we need to chose a representations
that allows us to build fast electronic circuits for
computer (e.g., adding)
• Since computer don't have fingers, they don't use
base 10 number.
• For computer binary number (1 and 0) work great
-- why? two-state devices
9/28/2023 6
Computer Architecture
Dr. Rahma Bouaziz, maître-assistant, FSG
A.U. 2023_2024
Chapter 2 – Part 1
Numbering system and
coding
Digital Computer Systems
● Digital systems consider discrete amounts of data
● Examples
● 26 letters in the alphabet
● 10 decimal digits
● Larger quantities can be built from discrete values:
● Words made of letters
● Numbers made of decimal digits (e.g. 239875.32)
9/28/2023 3
, In the Beginning
• In the beginning people represented numbers
base 10 because we have ten fingers.
9/28/2023 4
Understanding Decimal Numbers
● Decimal numbers are made of decimal digits:
(0,1,2,3,4,5,6,7,8,9) Base = 10
● But how many items does a decimal number
represent?
● 8653 = 8 x103 + 6 x102 + 5 x101 + 3 x100
● Number = d3 x B3 + d2 x B2 + d1 x B1 + d0 x B0 = Value
● What about fractions?
● 97654.35 = 9x104 + 7x103 + 6x102 + 5x101 + 4x100 + 3x10-1 + 5x10-2
● In formal notation → (97654.35)10
9/28/2023 5
Ways to "represent" a number…
• There are many ways to "represent" a number
ignored in life but important for computers.
• Representation does not affect the result of an
operation but representation affects difficulty of
computing result
• For computer we need to chose a representations
that allows us to build fast electronic circuits for
computer (e.g., adding)
• Since computer don't have fingers, they don't use
base 10 number.
• For computer binary number (1 and 0) work great
-- why? two-state devices
9/28/2023 6
