3. Add the following binary. (1000)2 and (101)2
Answers
Answer:
the correct answer is 10101010...
Concept:
Addition of binary numbers.
Binary numbers - Binary numbers are the numbers represented in base 2 numeral system. These numbers have only two digits 0 and 1. Whole computer world works on binary numbers.
The addition of binary numbers follows some rules.
a.) 0 + 0 = 0
b.) 0 + 1 = 1
c.) 1 + 0 = 1
d.) 1 + 1 = 0 (1 carry)
Given:
The given binary numbers are (1000)₂ and (101)₂.
Find:
Add the given numbers and find the answer.
Solution:
(1000)₂ + (101)₂ = 1 0 0 0
+ 1 0 1
1 1 0 1
∴ (1000)₂ + (101)₂ = (1101)₂
Verification:
To verify the answer, we will convert every binary number into decimal form.
L.H.S.
(1000)₂ in decimal form = 1×2³ + 0×2² + 0×2¹ + 0×2⁰
= 8 + 0 + 0 + 0 = (8)₁₀
(101)₂ in decimal form = 1×2² + 0×2¹ + 1×2⁰
= 4 + 0 + 1 = (5)₁₀
Now, L.H.S. = (1000)₂ + (101)₂ = (8)₁₀ + (5)₁₀ = (13)₁₀
R.H.S.
(1101)₂ in decimal form = 1×2³ + 1×2² + 0×2¹ + 1×2⁰
= 8 + 4 + 0 + 1
= (13)₁₀
R.H.S. = (1101)₂ = (13)₁₀
L.H.S. = R.H.S.
Hence verified.
So, (1000)₂ + (101)₂ = (1101)₂.
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