Module 5: Digital Techniques and
Electronic Instrument Systems
5.2 Numbering Systems
Number and Base
Base: How many symbols (digits) are used in the
current numbering system?
e.g. if the base of a number is 10, we use (maximum) 10
symbols to display this number.
if the base of a number is 8, we use 8 symbols to display
this number. (0, 1, 2, 3, 4, 5, 6, 7).
Examples: 1578, 1808210, 1001012.
MSD and LSD
In every numbering system, the value of a digit is
determined not only by its symbol, but also by its
The first digit of a number is called Most Significant digit (MSD).
The last digit of a number is called Less Significant digit (LSD).
Binary System Rules
0 + 0 = 0
1 + 0 = 1
0 + 1 = 1
1 + 1 = 0 and 1 carry.
0 – 0 = 0
1 – 0 = 1
0 – 1 = 1 with 1 carry
1 – 1 = 0
Get the complementary
of the subtrahend.
Discard any carries that
exceed the size of the
Numbering System Conversions
Decimal to digital:
I divide the decimal number by 2
I repeatedly divide the result by 2, until the dividend
The residue of each division in reverse order is the binary
Digital to decimal:
In the first digit d0 of the binary number I assign d0 *20.
In the nth digit of the binary number I assign dn *2n.
The sum: d0*20+ d1*21 + … + dn*2n is the decimal number.
Octal, Hex number conversion:
The same methodology, but “2” is replaced with “8” and