IEEE addition and subtraction

Explanation

Here is an explanation of the program:

1. Purpose

This program takes two floating-point numbers, performs either addition or subtraction based on user choice, and displays the result both as a decimal number and in its standard 32-bit IEEE 754 binary format.

2. Key Concepts

• IEEE 754 Single-Precision Standard: A 32-bit format consisting of 1 Sign bit, 8 Exponent bits, and 23 Mantissa/Fraction bits.
• Pointer Type Casting (Type Punning): C does not allow bitwise operations directly on float types. Casting (unsigned int *)&n allows the program to read the raw 32-bit representation of the float as an integer.
• Bitwise Operations: Using the right-shift (>>) and bitwise AND (&) operators to inspect individual bits from MSB (bit 31) to LSB (bit 0).

3. Code Walkthrough

• unsigned int *p = (unsigned int *)&n;
  Points to the exact same 32 bits of memory where the float n is stored, but treats them as an unsigned int so bitwise operations can be used.

• for(i = 31; i >= 0; i--)
  Loops through all 32 bits from left to right (most significant bit to least significant bit).

• (*p >> i) & 1
  Shifts the bit at position i to the units place and isolates it using & 1, printing either 0 or 1.

• if(i == 31 || i == 23) printf(" ");
  Inserts spaces to visually split the binary number into the three IEEE 754 fields:

  • Bit 31: Sign (1 bit)
  • Bits 30–23: Exponent (8 bits)
  • Bits 22–0: Mantissa / Fraction (23 bits)

• main()
  Prompts the user for two floats and an operator (+ or -), computes the result, and calls ieee() to print the bit-level representation.

4. Output

Example Run:

Enter two numbers: 5.5 2.25
+ or - +
Result = 7.75
IEEE 754 = 0 10000001 11110000000000000000000

• Sign (0): Positive number.
• Exponent (10000001): $129 - 127 = 2$ (meaning $2^2$).
• Mantissa (1111000...): Represents $.75 + .1875 + \dots = 0.9375$ (with implicit leading 1: $1.9375 \times 2^2 = 7.75$).