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Question

In the binary number system 100 + 1011 is equal to:


A
1000
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B
1011
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C
1110
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D
1111
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Solution

The correct option is D 1111
$$(100)_2 + (1011)_2 = (0 \times 2^0 + 0 \times 2^1 + 1 \times 2^2) + (1 \times 2^0 + 1 + 2^1 + 0 \times 2^2 + 1 \times 2^3)$$
= $$(0 + 0 +4) + (1 + 2 + 0 +8) = (15)_{10}$$
2     15
2      7      -1
2      3      -1 
2      1      -1
        0      -1
$$\uparrow$$ readup the remainders. or $$(15)_{10} = (1111)_2$$
ALTERNATIVELY :
0100 + 1011 = (1111)$$_2$$
$$(1111)_2 = 1 \times 2^3 + 1 \times  2^2 + 1 \times 2^1 +1 \times 2^0 = (15)_{10}$$

Physics
NCERT
Standard XII

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