How is the fractional part 0.432 converted?

Multiply by 2 repeatedly and read integer parts downward

Why is the binary answer for 37.432 only approximate?

The fraction never terminates, so it is cut after some bits

2074 Chaitra · 3 marks

Convert 37.432 decimal to binary

Short answer

Integer 37 by repeated division gives 100101. Fraction 0.432 by repeated multiplication yields about .0110111010. Thus (37.432)₁₀ ≈ (100101.0110111010)₂.

Convert 37.432 decimal number to binary.

Convert the integer and fraction parts separately.

Integer part: 37

Division	Quotient	Remainder
37 ÷ 2	18	1
18 ÷ 2	9	0
9 ÷ 2	4	1
4 ÷ 2	2	0
2 ÷ 2	1	0
1 ÷ 2	0	1

Reading upwards: $37 = 100101$ .

Fraction part: 0.432

Multiplication	Result	Bit
0.432 × 2	0.864	0
0.864 × 2	1.728	1
0.728 × 2	1.456	1
0.456 × 2	0.912	0
0.912 × 2	1.824	1
0.824 × 2	1.648	1
0.648 × 2	1.296	1
0.296 × 2	0.592	0
0.592 × 2	1.184	1
0.184 × 2	0.368	0

The fraction does not terminate, so we stop after 10 bits. Reading downwards: $0.432 \approx .0110111010$ .

Answer: $(37.432)_{10} \approx (100101.0110111010)_2$

Check: $100101.0110111010_2 = 37 + 442/1024 = 37.4316$ , very close to 37.432.

✓ Answer checked by Claude Opus 5.5 (high effort)

Convert octal 623.77 to decimal, binary, hex · Digital Logic, chapter 1
Convert (37.85)₁₀ to octal · Digital Logic, chapter 1
Gray vs binary code, convert (10110)₂ to Gray · Digital Logic, chapter 1
Convert (36.735)₈ to decimal · Digital Logic, chapter 1
Convert (10101)gray to decimal · Digital Logic, chapter 1
Convert (101101.011)₂ to decimal · Digital Logic, chapter 1
Decimal to binary conversion · Computer Programming, chapter 5
Binary to decimal in FORTRAN · Computer Programming, chapter 11
Number conversions 33 to binary etc. · Basic Electronics Engineering, chapter 6
Number conversions (375.37)8 etc. · Basic Electronics Engineering, chapter 6 · asked 3×

All Digital Logic chapter 1 questions →

Convert 37.432 decimal to binary

Integer part: 37

Fraction part: 0.432

Related questions