What is the precision of a 32-bit float?

About 7 significant decimal digits. The 23-bit mantissa gives 2^23 ≈ 8.4 million representable values per exponent range.

What does the exponent bias of 127 mean?

Stored exponent = actual exponent + 127. So exponent field 128 means 2^(128-127) = 2^1 = 2.

What is NaN in IEEE 754?

Not a Number: exponent all 1s (255) with non-zero mantissa. Used for undefined operations like 0/0.

IEEE 754 Single-Precision (32-bit) Float

Encode/decode IEEE 754 single-precision floats: 1 sign bit, 8 exponent bits (bias 127), 23 mantissa bits. Value = (-1)^s × 2^(e-127) × 1.mantissa.

Networking

Algorithms

Binary & Number

Systems

Dev Metrics

IP Subnet Calculator

IP Address

CIDR Prefix

Network

192.168.1.0

Broadcast

192.168.1.255

Subnet Mask

255.255.255.0

First Host

192.168.1.1

Last Host

192.168.1.254

Usable Hosts

254

Binary breakdown:

IP: 11000000.10101000.00000001.00000000

Mask: 11111111.11111111.11111111.00000000

Net: 11000000.10101000.00000001.00000000

How to Use

Enter the values for the scenario you are assessing. Encode/decode IEEE 754 single-precision floats: 1 sign bit, 8 exponent bits (bias 127), 23 mantissa bits. Value = (-1)^s × 2^(e-127) × 1.mantissa. Use the ieee 754 float32 result to inform your calculation.

Related Calculators

IEEE 754 Double64

Computer & IT

Binary → Hex