Chapter 2, Problem 33E

Program Plan Intro

a.

Decimal number:

• A decimal number is a number in which the whole number part and the fractional part is separated by a decimal point.
• The dot is known as a decimal point of a decimal number.
• Hence decimal numbering system is a method for representing both integer and non-integer numbers.

Binary number:

• Binary number is a number which is expressed in base-2 numeral system or binary numeral system.
• It uses only two symbols zero and one.
• It is mainly used by all modern computers and computer based devices.
• Each digit in binary numeral system is referred to as bit.

Explanation of Solution

b.

Conversion of decimal number 69 into binary value:

• Divide the number 69 by 2 and it returns 34 as quotient and 1 as remainder.
• Divide number 34 by 2 and it returns 17 as quotient and 0 as remainder.
• Divide number 17 by 2 and it returns 8 as quotient and 1 as remainder.
• Divide number 8 by 2 and it returns 4 as quotient and 0 as remainder.
• Divide number 4 by 2 and it returns 2 as quotient and 0 as remainder...

Explanation of Solution

c.

Conversion of decimal number 1066 into binary value:

• Divide the number 1066 by 2 and it returns 533 as quotient and 0 as remainder.
• Divide number 533 by 2 and it returns 266 as quotient and 1 as remainder.
• Divide number 266 by 2 and it returns 133 as quotient and 0 as remainder.
• Divide number 133 by 2 and it returns 66 as quotient and 1 as remainder.
• Divide number 66 by 2 and it returns 33 as quotient and 0 as remainder.
• Divide number 33 by 2 and it returns 16 as quotient and 1 as remainder.
• Divide number 16 by 2 and it returns 8 as quotient and 0 as remainder...

Explanation of Solution

d.

Conversion of decimal number 99 into binary value:

• Divide the number 99 by 2 and it returns 49 as quotient and 1 as remainder.
• Divide number 49 by 2 and it returns 24 as quotient and 1 as remainder.
• Divide number 24 by 2 and it returns 12 as quotient and 0 as remainder.
• Divide number 12 by 2 and it returns 6 as quotient and 0 as remainder.
• Divide number 6 by 2 and it returns 3 as quotient and 0 as remainder...

Explanation of Solution

e.

Conversion of decimal number 1 into binary value:

• Divide the number 1 by 2 and it is not possible because 1 is lesser than 2...