Chapter 2, Problem 32E

Program Plan Intro

a.

Decimal numbers:

• 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 numeral system is a method for representing both integer and non-integer numbers.

Octal numbers:

• Octal number system is also known as base 8 number system and uses the digits 0 to 7.
• These are made from binary numerals by grouping consecutive binary digits into three groups starting from the right.
• Octal numbers also make it easy to write large binary numbers into smaller groups.

Explanation of Solution

b.

Conversion of decimal number 321 into octal value:

• Since it is octal, divide the number 321 by 8 repeatedly. It returns 40 as quotient and 1 as remainder.
• Now divide 40 by 8 and it returns 5 as quotient and 0 as remainder.
• Now divide 5 by 8 and it is not possible as 5 is less than 8...

Explanation of Solution

c.

Conversion of decimal number 1492 into octal number:

• Since it is octal, divide the number 1492 by 8 repeatedly. It returns 186 as quotient and 4 as remainder.
• Now divide 186 by 8 and it returns 23 as quotient and 2 as remainder.
• Now divide 23 by 8 and it returns 2 as quotient and 7 as remainder...

Explanation of Solution

d.

Conversion of decimal number 1066 into octal number:

• Since it is octal, divide the number 1066 by 8 repeatedly. It returns 133 as quotient and 2 as remainder.
• Now divide 133 by 8 and it returns 16 as quotient and 5 as remainder.
• Now divide 16 by 8 and it returns 2 as quotient and 0 as remainder...

Explanation of Solution

e.

Conversion of decimal number 2001 into octal number:

• Since it is octal, divide the number 2001 by 8 repeatedly. It returns 250 as quotient and 1 as remainder.
• Now divide 250 by 8 and it returns 31 as quotient and 2 as remainder.
• Now divide 31 by 8 and it returns 3 as quotient and 7 as remainder...