Sum of the two binary numbers (100010)2 and (11011)2 is

Question

Sum of the two binary numbers (100010)2 and (11011)2 is (A)  (111111)2  (B)  (101111)2  (C)  (111001)2  (D)  (111101)2

Tardigrade Admin · Accepted Answer

Binary numeral system is also known as base

2

numerals.
The given number is first converted from binary to decimal equivalence

(100010)_{2} = 2^{5} \times 1 + 2^{4} \times 0 + 2^{3} \times 0 + 2^{2} \times 0 + 2^{1} \times 1 + 2^{o} \times 0

= 32 + 0 + 0 + 2 + 0

= (34)_{10}

and

(11011)_{2} = 2^{4} \times 1 + 2^{3} \times 1 + 2^{2} \times 0 + 2^{1} \times 1 \times 2^{o} \times 1

= 16 + 8 + 0 + 2 + 1

= (27)_{10}

∴

Sum

(100010)_{2} + (11011)_{2}

= (34)_{10} + (27)_{10}

= (61)_{0}

Now,

∴

Required sum (in binary system)

(100010)_{2} + (11011)_{2} = (111101)_{2}

Q. Sum of the two binary numbers $(100010)_{2}$ and $(11011)_{2}$ is