What is a number system in digital electronics?

• A number system is a way of writing any number.
• It can be represented by using any symbols or digits.
• It provides distinctive representation for each number.
• We can calculate value of any digit with the help of its position and base value.

Decimal Number System

• This is the most commonly used number system with base value of ten.
• It uses ten digits from 0 to 9.
• The leftmost position from decimal is units, tens, hundred and so on.
• The number 5312 has 2 in units place, 1 in tens place, 3 in hundreds place and 5 in thousands place.
• We can also express the number as

(5×1000) + (3×100) + (1×10) + (2×l)

=(5×10³) + (3×10²) + (1×10¹) + (2×l0⁰)

=5000 + 300 + 10 + 2

=5312

Binary Number System

• This number system has only two digits 0 and 1.
• The base of the binary number system is 2.
• The position of each number is the power of the base.

Convert 10101₂ to decimal number?

Step	Binary Number	Decimal Number
Step 1	101012	((1 × 24) + (0 × 23) + (1 × 22) + (0 × 21) + (1 × 20))10
Step 2	101012	(16 + 0 + 4 + 0 + 1)10
Step 3	101012	2110

Note: We can write 10111₂ as 10111.

Octal Number System

• The base value of this number system is eight.
• It has total eight digits from 0 to 7.
• Therefore we call it the octal number systems.
• The position of each number is the power of the base.

Convert 12569₈ to decimal number?

Step	Octal Number	Decimal Number
Step 1	125698	((1 × 84) + (2 × 83) + (5 × 82) + (6 × 81) + (9 × 80))10
Step 2	125698	(4096 + 1024 + 320 + 48 + 9)10
Step 3	125698	549710

Note: We can write 12575₈ as 12575 in octal.

Hexadecimal Number Systems

• This number system consists of ten digits and six letters.
• The digits are 0-9 and letters A-F.
• The value of these letters in the form of numbers is given as A = 10, B = 11, C = 12, D = 13, E = 14, F = 15.
• The base value of this number system is sixteen.
• The position of each number is equal to the power of the base.

Convert 19FBA₁₆ to decimal number?

Step	Hexadecimal Number	Decimal Number
Step 1	19FBA16	((1 × 164) + (9 × 163) + (F × 162) + (B × 161) + (A × 160))10
Step 2	19FBA16	((1 × 164) + (9 × 163) + (15 × 162) + (11 × 161) + (10 × 160))10
Step 3	19FBA16	(65536 + 36864 + 3840 + 176 + 10)10
Step 4	19FDA16	10642610

Note: We can write 19FDA₁₆ as 19FDA in hexadecimal.

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