Question

The number of 8 bit strings that can be formed beginning with either “111...” or “101...” is
1. 32
2. 64
3. 128
4. 256

Answer 1

Correct Answer - Option 2 : 64

A number system includes the number of independent digits used in the number system (the base), the place values of the different digits constituting the number, and the maximum numbers that can be written with the given number of digits.

The Binary Number System: 

• The binary number system with only two independent digits, 0 and 1, is a base-2 number system.
• All larger binary numbers are represented in terms of ‘0’ and ‘1’.

• The number of 8-bit strings beginning with 111 is 32.The 
• First 3 bits are fixed and the remaining 5 bits can be 0 or 1.
• So the total combinations are 2⁵=32
• The same is the case with the strings starting with 101.
• So the total number of strings is 32+32=6432+32=64.

Hence, the number of 8-bit strings that can be formed beginning with either “111...” or “101...” is 64.