Question

The number 110000000.010.....000 represented in IEEE single precision format corresponds to the decimal number

• A. -2.5
• B. -1.25
• C. -2.15
• D. -2.75

Hint:

Always remember the IEEE single-precision format: sign bit, exponent and mantissa.

Answer 1

The Correct Option is A

Step 1: In IEEE single-precision format, the first bit represents the sign (1 for negative, 0 for positive), the next 8 bits are the exponent, and the remaining 23 bits are the mantissa. 
Step 2: The given representation is: \[ 1 { } 10000000 { } 010...000 \] Sign bit is 1, thus it is a negative number. Exponent bits are \( 10000000 = 128\). The bias for single precision is 127, so exponent \( E = 128 - 127 = 1 \). Mantissa is \(1.01\), where we need to add 1 before the mantissa. 
Step 3: The decimal value is \[ (-1)^1 \times (1.25) \times 2^1 = -1 \times 1.25 \times 2 = -2.5 \]