Binary Converter

How do you convert decimal to binary by hand?

Divide the decimal number by 2, write the remainder, then divide the quotient by 2 again and repeat until the quotient reaches 0. Reading the remainders from the bottom up gives the binary string. Here is 156 worked all the way down; the remainder column read upward is 10011100.

Read the remainder column from the last row to the first: 1, 0, 0, 1, 1, 1, 0, 0 — so 156 in binary is 10011100.

How do you convert binary to decimal?

Each bit carries a place value that doubles from right to left. Write the weights above the bits and add the weights that sit over a 1. In 10011100 the 1s stand over 128, 16, 8 and 4, and 128 + 16 + 8 + 4 = 156.

Binary, decimal, octal and hexadecimal conversion chart

The first sixteen values are the ones worth memorising, because one hexadecimal digit is exactly four bits. The landmark rows below them are the boundaries you meet in real code: a full byte, a signed byte, two bytes and a kibibyte (1024 bytes).

How do you convert binary to hexadecimal and octal?

Group the bits instead of doing arithmetic. For hexadecimal take four bits at a time from the right, padding the left with zeros: 110110111 becomes 0001 1011 0111 = 1B7. For octal take three bits at a time: 110 110 111 = 667. Both equal 439 in decimal, and both conversions run the other way by expanding each digit back into its group of bits.

How does binary convert to text and ASCII?

Characters are stored as numbers, so binary becomes text in two steps: split the stream into 8-bit bytes, then look each byte up in the character table. RFC 20 fixes the classic 7-bit ASCII codes that UTF-8 still reuses for English, so 01001000 01101001 is 72 105, which spells "Hi".

How do you write an IP address in binary?

An IPv4 address is four 8-bit octets, so convert each number separately and pad every one to eight bits. 192.168.1.1 becomes 11000000.10101000.00000001.00000001. The padding is what makes prefixes readable: a /24 mask keeps the first 24 bits, which is 255.255.255.0, and a /27 mask ends mid-octet at 224 = 11100000.

How are negative numbers stored in binary?

Almost every processor uses two’s complement: write the positive value, flip every bit, then add 1. For −5 in eight bits, 00000101 flips to 11111010 and becomes 11111011. The leftmost bit acts as the sign, so an 8-bit signed range is −128 to 127 while the same 8 bits unsigned run 0 to 255. This converter works in unsigned whole numbers, so type 251 to see the bit pattern of −5.

Sources

The character codes, binary prefixes and address formats used on this page come from these specifications.

• RFC 20 — ASCII format for network interchange (character codes 0–127)
• NIST — Prefixes for binary multiples (kibi, mebi, gibi vs kilo, mega, giga)
• RFC 4648 — The Base16, Base32 and Base64 data encodings
• RFC 791 — Internet Protocol, the 32-bit IPv4 address format