1. The problem is to write the decimal number -4.3 in IEEE 754 single-precision floating-point format. 2. IEEE 754 single-precision format uses 32 bits: 1 bit for sign, 8 bits for exponent, and 23 bits for fraction (mantissa). 3. Step 1: Determine the sign bit. Since the number is negative, the sign bit is 1. 4. Step 2: Convert the absolute value 4.3 to binary. 4 in binary is $100$. 0.3 in binary is calculated by multiplying by 2 repeatedly: $0.3 \times 2 = 0.6$ (bit 0) $0.6 \times 2 = 1.2$ (bit 1) $0.2 \times 2 = 0.4$ (bit 0) $0.4 \times 2 = 0.8$ (bit 0) $0.8 \times 2 = 1.6$ (bit 1) $0.6 \times 2 = 1.2$ (bit 1) So fractional bits start as 0.010011... 5. Combining integer and fractional parts, 4.3 in binary is approximately: $100.0100110011...$ 6. Step 3: Normalize the binary number to the form $1.xxxxx \times 2^E$. Move the binary point 2 places left: $1.000100110011... \times 2^2$ 7. Step 4: Calculate the biased exponent. Bias for single precision is 127. Exponent $E = 2$, so biased exponent = $2 + 127 = 129$. 8. Step 5: Convert biased exponent to 8-bit binary: $129_{10} = 10000001_2$ 9. Step 6: Determine the mantissa (fractional part after the leading 1): Mantissa bits are the bits after the binary point in normalized form: $000100110011...$ Take the first 23 bits: $00010011001100110011001$ 10. Step 7: Assemble the IEEE 754 representation: Sign bit: 1 Exponent: 10000001 Mantissa: 00010011001100110011001 11. Final IEEE 754 binary representation: $1\ 10000001\ 00010011001100110011001$ 12. In hexadecimal, grouping bits by 4: $1100\ 0000\ 1000\ 1001\ 1001\ 1001\ 1001\ 1001$ Which is $C0 89 99 99$ in hex. Answer: The IEEE 754 single-precision representation of -4.3 is $\boxed{11000000100010011001100110011001}$ or hex $C0899999$.