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What is (1110011)2 ÷ (10111)2 equal to ?

A.
(101)2
B.
(1001)2
C.
(111)2
D.
(1011)2

Solution:

Concept:Binary to decimal conversion formulaN = bn-1 × 2n-1 + b4 × 24 + b3 × 23 + b2 × 22 + b1 × 21 + b0 × 20 Where N is decimal equivalent, b is the binary digit, 2 is the base valueDecimal to Binary conversionStep 1: Divide the decimal number n by 2. Use the integer quotient obtained in this step as the dividend for the next step.Step 2: Write the remainder from bottom to top i.e. in the reverse chronological order.Calculation:We know that, binary to decimal conversion formula isN = bn-1 × 2n-1 + b4 × 24 + b3 × 23 + b2 × 22 + b1 × 21 + b0 × 20 Now, converting (1110011)2 to decimal form, we get,(1110011)2 = 1 × 26 + 1 × 25 + 1 × 24 + 0 × 23 + 0 × 22 + 1 × 21 + 1 × 20 ? (1110011)2 = 64 + 32 + 16 + 2 + 1? (1110011)2 = 115 ------(i)Again converting (10111)2 to decimal form, we get,(10111)2 = 1 × 24 + 0 × 23 + 1 × 22 + 1 × 21 + 1 × 20? x + y = 16 + 4 + 2 + 1? x + y = 23 ------(ii)Putting the value of equations (i) and (ii), we get,We have to find (1110011)2 ÷ (10111)2Putting the value of equations (i) and (ii), we get,? 115 ÷ 23 = 5Now, convert the decimal number 5 into binary form, 5 = (101)2? (1110011)2 ÷ (10111)2 = (101)2

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