How do you write -7 in binary?

In 8-bit signed two's complement binary, -7 is 11111001. In 16-bit signed binary, it is 1111111111111001. To find this: take positive 7 (00000111 in 8-bit), invert every bit to get 11111000, and add 1 to obtain 11111001.

How do you convert a subnet mask to binary?

To convert an IPv4 subnet mask to binary, convert each of the 4 decimal octets into an 8-bit binary number separated by dots. For example, 255.255.255.0 becomes 11111111.11111111.11111111.00000000 (24 contiguous network 1-bits, known as a /24 prefix). A subnet mask of 255.255.255.192 becomes 11111111.11111111.11111111.11000000 (/26).

What is the difference between signed and unsigned binary?

Unsigned binary treats every bit as part of the positive magnitude, allowing an 8-bit number to range from 0 to 255. Signed binary uses the most significant bit (MSB) as a sign indicator (0 for positive, 1 for negative) via two's complement, allowing an 8-bit number to represent values from -128 to +127.

How do you convert decimal to binary manually?

To convert a decimal number to binary manually, divide the decimal integer by 2 repeatedly, recording the quotient and remainder at each step. Stop when the quotient reaches 0. Reading the remainders in reverse order (from bottom to top) gives the exact binary representation.

How does two's complement work for negative binary numbers?

Two's complement is the standard mathematical method digital hardware uses to store signed integers. To form the two's complement of a negative number: take the binary representation of the positive magnitude, invert every bit (change 0 to 1 and 1 to 0), and then add 1 to the result.

Binary Converter & Number Translator

Q: How do you write -4 in binary?

In computer systems using 8-bit signed two's complement representation, -4 in binary is 11111100. In 16-bit it is 1111111111111100, and in 32-bit it is 11111111111111111111111111111100. This is calculated by taking +4 (00000100), inverting all bits to get 11111011 (one's complement), and adding 1 to get 11111100.

Fast, accurate online binary converter. Convert between binary, decimal, hexadecimal, and octal with signed two's complement (-4, -7), IPv4 subnet mask to binary, and step-by-step calculation proofs.

Convert From

Convert To

Number Representation

Enter Number to Convert Decimal format: 0-9

Popular Numbers:

Negative (Two's Comp):

Binary Code:

Converted Value

All Base Representations

Binary (Base 2)

4-bit nibbles: -

Decimal (Base 10)

Standard magnitude

Hexadecimal (Base 16)

Prefix: 0x-

Octal (Base 8)

ASCII: -

Signed Two's Complement Formats

Essential for negative numbers in binary (-4, -7, etc.)

8-bit Signed (Range: -128 to 127):

16-bit Signed (-32,768 to 32,767):

32-bit Signed (Standard int):

Hex Two's Complement:

Step-by-Step Conversion Walkthrough

Division by 2 Proof

IPv4 Subnet Mask to Binary Converter

Convert IPv4 subnet masks or CIDR prefix notations directly into 32-bit binary octets. Essential for network engineers, CCNA students, and subnetting calculations.

Subnet Mask or CIDR Prefix

Quick Subnet Presets

32-Bit Binary Subnet Mask (4 Octets) CIDR: /24

Octet 1: 255

11111111

Octet 2: 255

11111111

Octet 3: 255

11111111

Octet 4: 0

00000000

Dotted Binary: 11111111.11111111.11111111.00000000

Network Bits (1s)

Identifies network portion

Host Bits (0s)

Available for host addressing

Wildcard Mask

0.0.0.255

Inverse of subnet mask

Usable Hosts

254

Formula: 2^H - 2

Bulk Batch Binary Converter

Convert a list of multiple values at once. Enter one value per line or separated by commas. All lines will be converted using the chosen bases and signed settings.

From Base

To Base

Enter Values (one per line)

#	Original Value	From Base	Converted Output	Action

Comprehensive Guide to Binary Conversion

Binary is the bedrock of modern electronic computing, digital microprocessors, and network telecommunications. While humans calculate in decimal (base 10) because we evolved with ten fingers, computers communicate using silicon transistors that exist in two physical states: electrical voltage on (represented by 1) or electrical voltage off (represented by 0).

Whether you are developing software, analyzing network packets, configuring routing subnets, or debugging low-level memory, converting between binary, decimal, octal, and hexadecimal is an essential daily skill.

The Four Essential Number Systems

Binary (Base 2): Uses only two symbols: 0 and 1. Each place value represents an ascending power of 2 ($2^0, 2^1, 2^2, 2^3 \dots$).
Octal (Base 8): Uses digits 0 through 7. Popular in Unix file permission strings (e.g. chmod 755). Each octal digit corresponds to exactly 3 binary bits.
Decimal (Base 10): The universal human counting system using digits 0 through 9.
Hexadecimal (Base 16): Uses digits 0–9 and letters A–F (where A=10, B=11, C=12, D=13, E=14, F=15). Each hex digit represents exactly 4 binary bits (one nibble).

Why Manual Conversion Causes Errors

Performing long division by 2 or positional power additions by hand is time-consuming and susceptible to simple arithmetic slips—especially when managing sign bits, two's complement carries, or 32-bit subnet octets.

Our free online binary converter eliminates human error by delivering instant, verified two-way conversions alongside full step-by-step mathematical proofs.

How to Convert Between Decimal and Binary Manually

Understand the two core mathematical algorithms used in computer science textbooks and technical exams:

Decimal to Binary (Successive Division by 2)

Divide the integer decimal number by 2.
Write down the integer quotient and the remainder (0 or 1).
Repeat the division with the quotient until the quotient reaches 0.
Read all remainders in reverse order (from bottom to top).

Worked Example: Decimal 21 to Binary

Division	Quotient	Remainder
21 ÷ 2	10	1 (LSB)
10 ÷ 2	5	0
5 ÷ 2	2	1
2 ÷ 2	1	0
1 ÷ 2	0	1 (MSB)

Result (read bottom-to-top): 10101₂

Binary to Decimal (Positional Weighting)

Write down the binary digits from right to left.
Assign an ascending power of 2 starting at $2^0 = 1$ for the rightmost bit.
Multiply each binary bit by its corresponding power of 2.
Sum all resulting products to get the decimal equivalent.

Worked Example: Binary 10101₂ to Decimal

(1 × 2⁴) + (0 × 2³) + (1 × 2²) + (0 × 2¹) + (1 × 2⁰)

= 16 + 0 + 4 + 0 + 1

= 21₁₀

Negative Numbers in Binary: Two's Complement Explained

How do digital systems represent negative values like -4 in binary or -7 in binary? In digital hardware, circuits cannot store a literal minus sign ("-"). Instead, computers universally rely on two's complement notation.

-4 in Binary (8-bit Step-by-Step)

Keyword Target

Start with +4 in 8-bit binary:
0000 0100
Invert every bit (One's Complement):
1111 1011
Add 1 to the inverted result:
1111 1011 + 1 = 1111 1100

Therefore, in 8-bit two's complement, -4 in binary is 11111100. In 16-bit it is 11111111 11111100, and in hex it is 0xFC.

-7 in Binary (8-bit Step-by-Step)

Keyword Target

Start with +7 in 8-bit binary:
0000 0111
Invert every bit (One's Complement):
1111 1000
Add 1 to the inverted result:
1111 1000 + 1 = 1111 1001

Therefore, in 8-bit two's complement, -7 in binary is 11111001. In 16-bit it is 11111111 11111001, and in hex it is 0xF9.

Why Bit-Width Matters: The same bit pattern 11111100 represents -4 in 8-bit signed two's complement, but represents 252 in unsigned binary! Always verify the bit-width (8-bit, 16-bit, 32-bit, or 64-bit) when writing firmware or decoding network packets.

Subnet to Binary: IPv4 Subnet Masks in Networking

In IPv4 computer networking, every IP address consists of 32 bits divided into four 8-bit octets. A subnet mask tells routers which bits identify the network and which bits identify individual hosts.

CIDR Prefix	Dotted Decimal Subnet Mask	32-Bit Binary Octets	Usable IP Hosts
/30	255.255.255.252	11111111.11111111.11111111.11111100	2
/29	255.255.255.248	11111111.11111111.11111111.11111000	6
/28	255.255.255.240	11111111.11111111.11111111.11110000	14
/26	255.255.255.192	11111111.11111111.11111111.11000000	62
/24	255.255.255.0	11111111.11111111.11111111.00000000	254
/16	255.255.0.0	11111111.11111111.00000000.00000000	65,534

Binary Code Translator: Reference Table (0 to 32)

Quick conversion lookup chart for Decimal, 8-Bit Binary, Hexadecimal, and Octal.

Decimal	Binary (8-bit)	Hexadecimal	Octal
0	00000000	0x0	0
1	00000001	0x1	1
2	00000010	0x2	2
3	00000011	0x3	3
4	00000100	0x4	4
5	00000101	0x5	5
6	00000110	0x6	6
7	00000111	0x7	7
8	00001000	0x8	10
9	00001001	0x9	11
10	00001010	0xA	12
11	00001011	0xB	13
12	00001100	0xC	14
13	00001101	0xD	15
14	00001110	0xE	16
15	00001111	0xF	17
16	00010000	0x10	20
17	00010001	0x11	21
18	00010010	0x12	22
19	00010011	0x13	23
20	00010100	0x14	24
21	00010101	0x15	25
22	00010110	0x16	26
23	00010111	0x17	27
24	00011000	0x18	30
25	00011001	0x19	31
26	00011010	0x1A	32
27	00011011	0x1B	33
28	00011100	0x1C	34
29	00011101	0x1D	35
30	00011110	0x1E	36
31	00011111	0x1F	37
32	00100000	0x20	40

Frequently Asked Questions (FAQ)

In modern computing systems using 8-bit signed two's complement representation, -4 in binary is 11111100. In a 16-bit architecture, it is 1111111111111100, and in 32-bit it is 11111111111111111111111111111100. To calculate it: take positive 4 (00000100), invert all bits to obtain 11111011 (one's complement), and add 1 to get 11111100.

In 8-bit signed two's complement binary, -7 is 11111001. To compute it manually: take positive 7 (00000111 in 8 bits), invert each bit to produce 11111000, and add 1 to reach 11111001. In 16-bit systems, sign extension pads 1s to the left: 1111111111111001.

To convert an IPv4 subnet mask to binary, convert each decimal octet into an 8-bit binary number separated by dots. For instance, 255.255.255.0 converts to 11111111.11111111.11111111.00000000. A mask of 255.255.255.192 converts to 11111111.11111111.11111111.11000000. The number of leading 1-bits defines the CIDR prefix (e.g. /24 or /26).

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Binary Converter & Number Translator

All Base Representations

Signed Two's Complement Formats

Step-by-Step Conversion Walkthrough

IPv4 Subnet Mask to Binary Converter

Bulk Batch Binary Converter

Comprehensive Guide to Binary Conversion

The Four Essential Number Systems

Why Manual Conversion Causes Errors

How to Convert Between Decimal and Binary Manually

Decimal to Binary (Successive Division by 2)

Binary to Decimal (Positional Weighting)

Negative Numbers in Binary: Two's Complement Explained

-4 in Binary (8-bit Step-by-Step)

-7 in Binary (8-bit Step-by-Step)

Subnet to Binary: IPv4 Subnet Masks in Networking

Binary Code Translator: Reference Table (0 to 32)

Frequently Asked Questions (FAQ)

Was this tool helpful?

Comments

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