A 36-bit floating-point binary number has eight bits plus sign for the exponent and 26 bits plus sign for the mantissa. The mantissa is a normalized fraction. Numbers in the mantissa and exponent are in signed-magnitude re. What are the largest and smallest positive quantities that can be represented, excluding zero?
Answers
Answer :-
The range of number which it can accommodate for a 36-bit floating point binary number is as follows :-
2 bits reserved for sign
26 bits for mantissa
8 bits for exponent
So the range will be :-
- (1 -2⁻²⁶) x 2²⁵⁵ to (1 -2⁻²⁶) x 2²⁵⁵
Largest Quantity : (1 -2⁻²⁶) x 2²⁵⁵
Smallest Quantity : - (1 -2⁻²⁶) x 2²⁵⁵
Answer:
According to the given details, the normalized fraction as well as numbers in exponent and mantissa is actually in signed magnitude representation for the 36-bit floating point binary number.
In this process, two bits are actually reserved for a sign, 26-bits for mantissa and eight bits for exponent. The overall range of numbers which is accommodated is 255. The exponent value range of 36-bit number can range between -254 < E < 255.
Explanation: