Explain binary number system.

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Q. Explain binary number system.

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Binary system = base-2 numbers using only digits 0 and 1, with place values as powers of 2.

The binary number system is a positional number system with base 2. It uses only two symbols (digits): 0 and 1, each called a bit (binary digit).

The place value of each digit is a power of 2: from right to left $2^0, 2^1, 2^2, 2^3,\dots$
Example: the binary number $1011_2$ equals $1\times2^3+0\times2^2+1\times2^1+1\times2^0 = 8+0+2+1 = 11_{10}.$ …

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CBSE 2024Set A1 markMCQ
$Q. The equivalent number of decimal number 27 into binary number system will be (A) (10011)₂ (B) (10111)₂ (C) (11001)₂ (D) (11011)₂$
›Reveal solutionSolution
Decimal 27 converts to binary 11011 → option (D).

Repeatedly divide 27 by 2 and read the remainders from bottom up:

27 ÷ 2 = 13, remainder 1

13 ÷ 2 = 6, remainder 1

6 ÷ 2 = 3, remainder 0

3 ÷ 2 = 1, remainder 1 …
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CBSE 2023Set F1 markMCQ
$Q. The binary equivalent of 25 is (A) (1100)_2 (B) (1001)_2 (C) (11001)_2 (D) (11101)_2$
›Reveal solutionSolution
25 = 16 + 8 + 1 = 11001 in binary.

Convert 25 to binary by repeated division by 2:

25 ÷ 2 = 12 remainder 1

12 ÷ 2 = 6 remainder 0

6 ÷ 2 = 3 remainder 0

3 ÷ 2 = 1 remainder 1

1 ÷ 2 = 0 remainder 1 …
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CBSE 2022Set I1 markMCQ
$Q. Binary number of decimal number (8)_10 is (A) (1000)_2 (B) (1001)_2 (C) (111)_2 (D) (110)_2$
›Reveal solutionSolution
8 in decimal = 1000 in binary.

Convert 8 to binary by repeated division by 2:

8 ÷ 2 = 4, remainder 0

4 ÷ 2 = 2, remainder 0

2 ÷ 2 = 1, remainder 0

1 ÷ 2 = 0, remainder 1 …
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CBSE 2021Set A1 markMCQ
$Q. The decimal number of binary number (1001)₂ is (A) (12)₁₀ (B) (18)₁₀ (C) (9)₁₀ (D) (25)₁₀$
›Reveal solutionSolution

(1001)₂ = 9 in decimal.

Convert binary to decimal by multiplying each bit by its place value (powers of 2), starting from the right: …

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CBSE 2021Set A1 markMCQ
$Q. Which of the following is correct? (A) (1100)₂ = (12)₁₀ (B) (1001)₂ = (12)₁₀ (C) (1111)₂ = (12)₁₀ (D) (1011)₂ = (12)₁₀$
›Reveal solutionSolution
(1100)₂ = 8 + 4 = (12)₁₀.

Convert each binary number using place values $2^3, 2^2, 2^1, 2^0 = 8, 4, 2, 1$ :

$(1100)_2 = 1\cdot8 + 1\cdot4 + 0\cdot2 + 0\cdot1 = 12$ ✓

$(1001)_2 = 8 + 0 + 0 + 1 = 9$ …
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CBSE 2016Set ANNUAL1 mark
$Q. What is the decimal equivalent of the binary number 10011? OR Draw the symbol of a two-input NOR gate.$
›Reveal solutionSolution

Converting the binary number 10011 to decimal by place values gives 19.

Binary 10011 has place values (from right to left) 2⁰, 2¹, 2², 2³, 2⁴:

…

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Q.Explain binary number system.

Concept understanding — Decimal and Binary Number Systems

Q.Explain binary number system.

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