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What is the conversion of -1439 from decimal to binary base?
alphonsio

-1439 in binary (2's complement on 16 bits) is: 1111 1010 0110 0001

(1439)10=(1111 1010 0110 0001)2(-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 14391439 by 22 and note the remainder at each step:

  • 1439÷2=7191439 \div 2 = 719, remainder 1
  • 719÷2=359719 \div 2 = 359, remainder 1
  • 359÷2=179359 \div 2 = 179, remainder 1
  • 179÷2=89179 \div 2 = 89, remainder 1
  • 89÷2=4489 \div 2 = 44, remainder 1
  • 44÷2=2244 \div 2 = 22, remainder 0
  • 22÷2=1122 \div 2 = 11, remainder 0
  • 11÷2=511 \div 2 = 5, remainder 1
  • 5÷2=25 \div 2 = 2, remainder 1
  • 2÷2=12 \div 2 = 1, remainder 0
  • 1÷2=01 \div 2 = 0, remainder 1

Reading the remainders from bottom to top, the binary conversion of 14391439 is :

(1439)10=(10110011111)2(-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)

  • Inverted: 01001100000

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(-1439)_{10}=(1111~1010~0110~0001)_2