NIMCET 2014 — Computer PYQ

Solution

There are two common methods to solve this: direct binary multiplication or conversion to the decimal system.

Method 1: Conversion to Decimal

First, convert both binary numbers to their decimal equivalents, multiply them, and then convert the result back to binary.

• Step 1: Convert $111_2$ to decimal

  $$(111{)}_2=2^2+2^1+2^0=4+2+1=(7{)}_{10}$$

• Step 2: Convert $101_2$ to decimal

  $$(101{)}_2=2^2+2^0=4+1=(5{)}_{10}$$

• Step 3: Multiply the decimal numbers

  $$5\times 7=(35{)}_{10}$$

• Step 4: Convert $(35{)}_{10}$ back to binary

  $$(35{)}_{10}=32+2+1=2^5+2^1+2^0=(100011{)}_2$$