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To represent the number 6.5 in IEEE 754 single-precision (32-bit) floating point, we follow these steps:

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📌 Step 1: Convert 6.5 to binary

• 6 in binary = 110
• 0.5 in binary = .1
  → So, 6.5 = 110.1 in binary

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📌 Step 2: Normalize the binary number

We want it in the form of 1.xxxxx × 2^n.

110.1 → 1.101 × 2²
So:

• Mantissa (fraction) = 101 (rest filled with zeros)
• Exponent = 2

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📌 Step 3: Find the exponent bits

IEEE 754 uses a bias of 127 for single-precision:

• Exponent = 2 + 127 = 129
• 129 in binary = 10000001

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📌 Step 4: Assemble the IEEE 754 components

• Sign bit = 0 (since 6.5 is positive)
• Exponent = 10000001
• Mantissa (23 bits) = 10100000000000000000000

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✅ Final IEEE 754 representation of 6.5:

0 10000001 10100000000000000000000

import struct
# Convert 6.5 to IEEE 754 single-precision binary representation
num = 6.5
packed = struct.pack('>f', num)  # Big-endian float (4 bytes)
binary_rep = ''.join(f'{byte:08b}' for byte in packed)
hex_rep = packed.hex().upper()binary_rep, hex_rep