10 bit integer lies in the range of
Answers
Answer:
0 to 10232^10=1024
Given : 10 bit integer
To Find : range
Solution:
Assuming 10-bit unsigned integer
Least is
(0000000000)₂ = 0₁₀
Greatest is
(1111111111)₂ = 1023₁₀
How
( 1 * 2⁹ + 1 * 2⁸ + 1 * 2⁷ + 1 * 2⁶ + 1 * 2⁵ + 1 * 2⁴ + 1 * 2³ + 1 * 2² + 1 * 2¹ + 1 * 2⁰)
= ( 512 + 256 + 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 )
= 1023
Hence 10 bit integer lies in the range of [ 0 , 1023]
Shortcut :
n = number of bits
Maximum number in Decimal is 2ⁿ - 1
n = 10 hence max = 2¹⁰ - 1= 1023
Least is 0
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