Digital Principles and System Design MCQs | Page - 1

 on multiplying the decimal number continuously by 2, the binary equivalent is obtained by the collection of the integer part. however, if it’s an integer, then it’s binary equivalent is determined by dividing the number by 2 and collecting the remainders.

 binary coded decimal is a combination of 4 binary digits. for example-8421.

 the decimal number 10 is represented in its bcd form as 0001 0000, in accordance to 8421 for each of the two digits.

 first the two numbers are converted into their respective bcd form using 8421 sequence. then binary subtraction is carried out.

 when numbers, letters or words are represented by a special group of symbols, this process is called encoding. encoding in the sense of fetching the codes or words in a computer. it is done to secure the transmission of information.

 the number of bits needed to represent a given decimal number is always greater than the number of bits required for a straight binary encoding of the same. hence, a three digit decimal number requires 12 bits for representation in bcd format.

 total number of decimals to be represented = 10000 = 104 = 2n (where n is the number of bits required) = 213.29. therefore, the number of bits required for straight binary encoding = 14.

 the addition of ‘3’ to each digit yields the three new digits ‘8’, ’12’ and ’10’. hence, the corresponding four-bit binary equivalents are 100011001010, in accordance to 8421 format.

 the conversion of binary numbers into digits ‘1100’, ‘1010’, ‘0011’, ‘0111’ and ‘0101’ gives

 the expression for associative property is given by a+(b+c) = (a+b)+c & a*(b*c) = (a*b)*c.