Question

Convert the following two's complement numbers to a suitable form for human viewing (e.g. decimal).

F29D₁₆
Explain, please...

Answer 1

answer)

Given hex decimal number is F29D16

convert this hex to binary:process is take each letter in hexa and convert it into 4 bit binary

so F29D16 becomes :1111 0010 1001 1101 0001 0110

F=1111,2=0010,9=1001,D=1101,1=0001,6=0110

-->hear least significant bit is 1 so it represent the given number is negative

->next find the magnitude of the number. if we change the sign then we get magnitude of the given number.

changing sign means first find the one's complement then add 1 to given result .

1111 0010 1001 1101 0001 0110 becomes 000011010110001011101001+1=(0000 1101 0110 0010 1110 1010)₂=(0D62EA)₁₆=(A*16⁰+E*16¹+2*16²+6*16³+D*16⁴)=877290₁₀

So add '-' to given decimal then we get final answer.

so answer is -877290₁₀

or: add minus to last digit in binary number

(-1*2²³)+(1*2²²)+(1*2²¹)+(1*2²⁰)+ (0 × 2¹⁹) + (0 × 2¹⁸) + (1 × 2¹⁷) + (0 × 2¹⁶) + (1 × 2¹⁵) + (0 × 2¹⁴) + (0 × 2¹³) + (1 × 2¹²) + (1 × 2¹¹) + (1 × 2¹⁰) + (0 × 2⁹) + (1 × 2⁸) + (0 × 2⁷) + (0 × 2⁶) + (0 × 2⁵) + (1 × 2⁴) + (0 × 2³) + (1 × 2²) + (1 × 2¹) + (0 × 2⁰)= -877290₁₀