Signed: Binary -> Integer: 0010 0100 1010 0011 1111 1111 1101 1010 Signed Binary Number Converted and Written as a Decimal System Integer (in Base Ten)
The signed binary (in base two) 0010 0100 1010 0011 1111 1111 1101 1010(2) to an integer (with sign) in decimal system (in base ten) = ?
1. Is this a positive or a negative number?
In a signed binary, the first bit (the leftmost) is reserved for the sign,
1 = negative, 0 = positive. This bit does not count when calculating the absolute value.
0010 0100 1010 0011 1111 1111 1101 1010 is the binary representation of a positive integer, on 32 bits (4 Bytes).
2. Construct the unsigned binary number.
Exclude the first bit (the leftmost), that is reserved for the sign:
0010 0100 1010 0011 1111 1111 1101 1010 = 010 0100 1010 0011 1111 1111 1101 1010
3. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:
230
0 229
1 228
0 227
0 226
1 225
0 224
0 223
1 222
0 221
1 220
0 219
0 218
0 217
1 216
1 215
1 214
1 213
1 212
1 211
1 210
1 29
1 28
1 27
1 26
1 25
0 24
1 23
1 22
0 21
1 20
0
4. Multiply each bit by its corresponding power of 2 and add all the terms up.
010 0100 1010 0011 1111 1111 1101 1010(2) =
(0 × 230 + 1 × 229 + 0 × 228 + 0 × 227 + 1 × 226 + 0 × 225 + 0 × 224 + 1 × 223 + 0 × 222 + 1 × 221 + 0 × 220 + 0 × 219 + 0 × 218 + 1 × 217 + 1 × 216 + 1 × 215 + 1 × 214 + 1 × 213 + 1 × 212 + 1 × 211 + 1 × 210 + 1 × 29 + 1 × 28 + 1 × 27 + 1 × 26 + 0 × 25 + 1 × 24 + 1 × 23 + 0 × 22 + 1 × 21 + 0 × 20)(10) =
(0 + 536 870 912 + 0 + 0 + 67 108 864 + 0 + 0 + 8 388 608 + 0 + 2 097 152 + 0 + 0 + 0 + 131 072 + 65 536 + 32 768 + 16 384 + 8 192 + 4 096 + 2 048 + 1 024 + 512 + 256 + 128 + 64 + 0 + 16 + 8 + 0 + 2 + 0)(10) =
(536 870 912 + 67 108 864 + 8 388 608 + 2 097 152 + 131 072 + 65 536 + 32 768 + 16 384 + 8 192 + 4 096 + 2 048 + 1 024 + 512 + 256 + 128 + 64 + 16 + 8 + 2)(10) =
614 727 642(10)
5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
0010 0100 1010 0011 1111 1111 1101 1010(2) = 614 727 642(10)
The number 0010 0100 1010 0011 1111 1111 1101 1010(2) converted from a signed binary (base two) and written as an integer in decimal system (base ten):
0010 0100 1010 0011 1111 1111 1101 1010(2) = 614 727 642(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.
Convert signed binary numbers to integers in decimal system (in base ten)
The first bit (the leftmost) is reserved for the sign (1 = negative, 0 = positive) and it doesn't count when calculating the absolute value.
Binary number's length must be: 2, 4, 8, 16, 32, 64 - or else extra bits on 0 are added in front (to the left).
How to convert a signed binary number to an integer in base ten:
1) Construct the unsigned binary number: exclude the first bit (the leftmost); this bit is reserved for the sign, 1 = negative, 0 = positive and does not count when calculating the absolute value (without sign).
2) Multiply each bit of the binary number by its corresponding power of 2 that its place value represents.
3) Add all the terms up to get the positive integer number in base ten.
4) Adjust the sign of the integer number by the first bit of the initial binary number.