Chapter 2, Problem 23E

a.

Program Plan Intro

Conversion of a binary number from base 2 to base 10:

• To convert a number from base 2 to base 10, the following steps should be followed:
  • A binary number has two digits that is 0 and 1.
  • Process the binary number from left to right.
  • Convert every binary digit into its corresponding decimal value.

Conversion of a number from base 8 to base 10:

• To convert a number from base 8 to base 10, the following steps should be followed:
• A binary number has two digits 0 and 1.
• Process the number from left to right.
• Convert the number into its corresponding decimal value.

Conversion of a number from base 16 to base 10:

• To convert a number from base 16 to base 10, the following steps should be followed:
• Hexadecimal number has generally 16 digits from 0 to 9 and from 10 to 15 and it is represented in the form of letters from A to F.
• is the base of a hexadecimal number.
• Process the number from left to right.
• Convert the number into its corresponding decimal value.

Explanation of Solution

b.

Conversion of octal number 777 from base 8 to base 10:

• The octal number has 8 digits from 0 to 7.
• is an octal number. Hence base of an octal number is 8.
• Process the number from left to right.
• Convert every octal value to its corresponding decimal value...

Explanation of Solution

c.

Conversion of the number FEC from base 16 to base 10:

• A hexadecimal number has generally 16 digits from 0 to 9 and from 10 to 15 and it is represented in the form of letters from A to F.
• FEC is a hexadecimal number where C denotes 12, E denotes 14 and F denotes 15. The base of this number is 16 since this is a hexadecimal number.
• Process the number from left to right...

Explanation of Solution

d.

Conversion of the number 777 from base 16 to base 10:

• A hexadecimal number has generally 16 digits from 0 to 9 and from 10 to 15 and it is represented in the form of letters from A to F.
• is a hexadecimal number. The base of this number is 16 since this is a hexadecimal number.
• Process the number from left to right...

Explanation of Solution

e.

Conversion of octal number 111 from base 8 to base 10:

• The octal number has 8 digits from 0 to 7.
• is an octal number. Hence base of an octal number is 8.
• Process the number from left to right.
• Convert every octal value to its corresponding decimal value...