Signed Integer Converter

This conversion supports binary digits ranging from 0 to 32 bits, with the decimal number range from -2147483648 to -1.
Binary (base 2)
Decimal (base 10)
Hexadecimal (base 16)

Description

For the same number, the result of adding its negative and positive values should be 0. For example, for the number 7, -7 + 7 = 0, so -7 = 0 - 7, which can be represented in binary as -7 = 0000 - 0111 = 1001.

On the other hand, the binary representation of 7 is 0111. The one's complement of 0111 is 1000 and the two's complement (one's complement + 1) is 1001. Therefore, the binary representation of -7 is 1001, which matches the result obtained earlier.

From the perspective of the CPU, in an 8-bit data environment, a binary number like 11111001 can represent the decimal positive integer 249 or the decimal negative integer -7. Regardless of whether the CPU treats it as a positive or negative number during operations, the arithmetic results are always correct.

Signed integer encoding example (64 bit)
Decimal Decimal Binary (the first bit is the sign bit) Hexadecimal
-2^63 -9223372036854775808 10000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 0x8000000000000000
-2^62 -4611686018427387904 11000000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 0xC000000000000000
-2^61 -2305843009213693952 11100000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 0xE000000000000000
-2^60 -1152921504606846976 11110000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 0xF000000000000000
-2^59 -576460752303423488 11111000 00000000 00000000 00000000 00000000 00000000 00000000 00000000 0xF800000000000000
-2^58 -288230376151711744 11111100 00000000 00000000 00000000 00000000 00000000 00000000 00000000 0xFC00000000000000
-2^57 -144115188075855872 11111110 00000000 00000000 00000000 00000000 00000000 00000000 00000000 0xFE00000000000000
-2^56 -72057594037927936 11111111 00000000 00000000 00000000 00000000 00000000 00000000 00000000 0xFF00000000000000
-2^55 -36028797018963968 11111111 10000000 00000000 00000000 00000000 00000000 00000000 00000000 0xFF80000000000000
-2^54 -18014398509481984 11111111 11000000 00000000 00000000 00000000 00000000 00000000 00000000 0xFFC0000000000000
-2^53 -9007199254740992 11111111 11100000 00000000 00000000 00000000 00000000 00000000 00000000 0xFFE0000000000000
-2^52 -4503599627370496 11111111 11110000 00000000 00000000 00000000 00000000 00000000 00000000 0xFFF0000000000000
-2^51 -2251799813685248 11111111 11111000 00000000 00000000 00000000 00000000 00000000 00000000 0xFFF8000000000000
-2^50 -1125899906842624 11111111 11111100 00000000 00000000 00000000 00000000 00000000 00000000 0xFFFC000000000000
-2^49 -562949953421312 11111111 11111110 00000000 00000000 00000000 00000000 00000000 00000000 0xFFFE000000000000
-2^48 -281474976710656 11111111 11111111 00000000 00000000 00000000 00000000 00000000 00000000 0xFFFF000000000000
-2^47 -140737488355328 11111111 11111111 10000000 00000000 00000000 00000000 00000000 00000000 0xFFFF800000000000
-2^46 -70368744177664 11111111 11111111 11000000 00000000 00000000 00000000 00000000 00000000 0xFFFFC00000000000
-2^45 -35184372088832 11111111 11111111 11100000 00000000 00000000 00000000 00000000 00000000 0xFFFFE00000000000
-2^44 -17592186044416 11111111 11111111 11110000 00000000 00000000 00000000 00000000 00000000 0xFFFFF00000000000
-2^43 -8796093022208 11111111 11111111 11111000 00000000 00000000 00000000 00000000 00000000 0xFFFFF80000000000
-2^42 -4398046511104 11111111 11111111 11111100 00000000 00000000 00000000 00000000 00000000 0xFFFFFC0000000000
-2^41 -2199023255552 11111111 11111111 11111110 00000000 00000000 00000000 00000000 00000000 0xFFFFFE0000000000
-2^40 -1099511627776 11111111 11111111 11111111 00000000 00000000 00000000 00000000 00000000 0xFFFFFF0000000000
-2^39 -549755813888 11111111 11111111 11111111 10000000 00000000 00000000 00000000 00000000 0xFFFFFF8000000000
-2^38 -274877906944 11111111 11111111 11111111 11000000 00000000 00000000 00000000 00000000 0xFFFFFFC000000000
-2^37 -137438953472 11111111 11111111 11111111 11100000 00000000 00000000 00000000 00000000 0xFFFFFFE000000000
-2^36 -68719476736 11111111 11111111 11111111 11110000 00000000 00000000 00000000 00000000 0xFFFFFFF000000000
-2^35 -34359738368 11111111 11111111 11111111 11111000 00000000 00000000 00000000 00000000 0xFFFFFFF800000000
-2^34 -17179869184 11111111 11111111 11111111 11111100 00000000 00000000 00000000 00000000 0xFFFFFFFC00000000
-2^33 -8589934592 11111111 11111111 11111111 11111110 00000000 00000000 00000000 00000000 0xFFFFFFFE00000000
-2^32 -4294967296 11111111 11111111 11111111 11111111 00000000 00000000 00000000 00000000 0xFFFFFFFF00000000
-2^31 -2147483648 11111111 11111111 11111111 11111111 10000000 00000000 00000000 00000000 0xFFFFFFFF80000000
-2^30 -1073741824 11111111 11111111 11111111 11111111 11000000 00000000 00000000 00000000 0xFFFFFFFFC0000000
-2^29 -536870912 11111111 11111111 11111111 11111111 11100000 00000000 00000000 00000000 0xFFFFFFFFE0000000
-2^28 -268435456 11111111 11111111 11111111 11111111 11110000 00000000 00000000 00000000 0xFFFFFFFFF0000000
-2^27 -134217728 11111111 11111111 11111111 11111111 11111000 00000000 00000000 00000000 0xFFFFFFFFF8000000
-2^26 -67108864 11111111 11111111 11111111 11111111 11111100 00000000 00000000 00000000 0xFFFFFFFFFC000000
-2^25 -33554432 11111111 11111111 11111111 11111111 11111110 00000000 00000000 00000000 0xFFFFFFFFFE000000
-2^24 -16777216 11111111 11111111 11111111 11111111 11111111 00000000 00000000 00000000 0xFFFFFFFFFF000000
-2^23 -8388608 11111111 11111111 11111111 11111111 11111111 10000000 00000000 00000000 0xFFFFFFFFFF800000
-2^22 -4194304 11111111 11111111 11111111 11111111 11111111 11000000 00000000 00000000 0xFFFFFFFFFFC00000
-2^21 -2097152 11111111 11111111 11111111 11111111 11111111 11100000 00000000 00000000 0xFFFFFFFFFFE00000
-2^20 -1048576 11111111 11111111 11111111 11111111 11111111 11110000 00000000 00000000 0xFFFFFFFFFFF00000
-2^19 -524288 11111111 11111111 11111111 11111111 11111111 11111000 00000000 00000000 0xFFFFFFFFFFF80000
-2^18 -262144 11111111 11111111 11111111 11111111 11111111 11111100 00000000 00000000 0xFFFFFFFFFFFC0000
-2^17 -131072 11111111 11111111 11111111 11111111 11111111 11111110 00000000 00000000 0xFFFFFFFFFFFE0000
-2^16 -65536 11111111 11111111 11111111 11111111 11111111 11111111 00000000 00000000 0xFFFFFFFFFFFF0000
-2^15 -32768 11111111 11111111 11111111 11111111 11111111 11111111 10000000 00000000 0xFFFFFFFFFFFF8000
-2^14 -16384 11111111 11111111 11111111 11111111 11111111 11111111 11000000 00000000 0xFFFFFFFFFFFFC000
-2^13 -8192 11111111 11111111 11111111 11111111 11111111 11111111 11100000 00000000 0xFFFFFFFFFFFFE000
-2^12 -4096 11111111 11111111 11111111 11111111 11111111 11111111 11110000 00000000 0xFFFFFFFFFFFFF000
-2^11 -2048 11111111 11111111 11111111 11111111 11111111 11111111 11111000 00000000 0xFFFFFFFFFFFFF800
-2^10 -1024 11111111 11111111 11111111 11111111 11111111 11111111 11111100 00000000 0xFFFFFFFFFFFFFC00
-2^9 -512 11111111 11111111 11111111 11111111 11111111 11111111 11111110 00000000 0xFFFFFFFFFFFFFE00
-2^8 -256 11111111 11111111 11111111 11111111 11111111 11111111 11111111 00000000 0xFFFFFFFFFFFFFF00
-2^7 -128 11111111 11111111 11111111 11111111 11111111 11111111 11111111 10000000 0xFFFFFFFFFFFFFF80
-2^6 -64 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11000000 0xFFFFFFFFFFFFFFC0
-2^5 -32 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11100000 0xFFFFFFFFFFFFFFE0
-2^4 -16 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11110000 0xFFFFFFFFFFFFFFF0
-2^3 -8 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111000 0xFFFFFFFFFFFFFFF8
-2^2 -4 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111100 0xFFFFFFFFFFFFFFFC
-2^1 -2 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111110 0xFFFFFFFFFFFFFFFE
-2^0 -1 11111111 11111111 11111111 11111111 11111111 11111111 11111111 11111111 0xFFFFFFFFFFFFFFFF