-1439 in binary (2's complement on 16 bits) is: 1111 1010 0110 0001
(−1439)10=(1111 1010 0110 0001)2
To convert the number -1439 from decimal to binary, we first convert the positive number 1439 to binary, then encode the negative sign (2's complement).
1. absolute value conversion (1439)
Let's divide 1439 by 2 and note the remainder at each step:
- 1439÷2=719, remainder 1
- 719÷2=359, remainder 1
- 359÷2=179, remainder 1
- 179÷2=89, remainder 1
- 89÷2=44, remainder 1
- 44÷2=22, remainder 0
- 22÷2=11, remainder 0
- 11÷2=5, remainder 1
- 5÷2=2, remainder 1
- 2÷2=1, remainder 0
- 1÷2=0, remainder 1
Reading the remainders from bottom to top, the binary conversion of 1439 is :
(−1439)10=(10110011111)2
2. Negative sign
The negative sign is represented by the 2's complement. Invert each bit and add 1 to the result:
Step 1: invert the bits of 14401439 (10110011111)
Step 2 : Add 1
- 01001100000 + 1 = 01001100001
Step 3 : Complete with 1s
- Add 1's to obtain a 16-bit representation: 1111 1010 0110 0001
On 16 bits, this gives :
(−1439)10=(1111 1010 0110 0001)2