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Number System: Some Numerical problem

1. If the decimal expression ${\mathbf{(}{\mathbf{16}}^{\mathbf{3}}\mathbf{ }\mathbf{X}\mathbf{ }\mathbf{9}\mathbf{ }\mathbf{+}\mathbf{ }{\mathbf{16}}^{\mathbf{1}}\mathbf{ }\mathbf{X}\mathbf{ }\mathbf{7}\mathbf{ }\mathbf{+}\mathbf{ }\mathbf{3}\mathbf{)}}_{\mathbf{10}}$ is converted to Binary, what is the relation between the number of 1’s and 0’s?

Solution:

No. of 1s = 7

No. of 0s = 9

2. If a binary number is 126 bits, how many digits are required to represent that binary number in decimal?

Solution:

Maximum binary numbers that can be represented with 126 bits = $(2^{126} - 1)$ say, ‘d’ digits are required in decimal to represent $(2^{126} - 1)$

Therefore, Maximum decimal numbers with d – digits.

∴ At least 38-digits are required in decimal to represent any binary number with 126 bits.

3. How many bits are used to represent a 24-digit decimal number in binary?

Solution:

Solution:

And,