# convert A=12.5(Decimal) and B=1.6(hexadecimal) into binary format and perform following operation

#### jeoboo

Joined Apr 8, 2017
5
convert A=12.5(Decimal) and B=1.6(hexadecimal) into binary format employing 6 bits for the integer part and 3 for the fractional part, including the sign bit. Perform following operation
1)C=-A-B (using signed 1's complement)
2)D=-A+B(using signed 2's complement)
3)A-B(using 9's complement)

that is what i've tried
1)i convert A and B into binary, which are A=001100.100,B=000001.011.
-A-B=+(-A)+(-B)
1's complement of A is 110011.011, and 1's complement of B is 111110.100
and then 110011.011+111110.100=1110001.111(carry 1 ), so 110001.111+1=110010.111

2)-A+B=+(-A)+B
2's complement of A is 110100.011
so 110100.011+000001.011=110101.110

i don't know if these are correct or not, thanks for help

also how do i do the number 3, with 9's complement

#### WBahn

Joined Mar 31, 2012
24,700
So how might you determine if 110010.111 is the correct answer? What value does it represent in decimal? What value is C in decimal given the values for A and B? Do they agree?

You might consider whether, in general, you can add two 1's complement numbers the same way you add two unsigned binary numbers?

Hint: What are the 4-bit 1's complement representations for 5 and -5? What happens if you add them?

This gets at the very heart of why we use two's complement.

The term "9's complement" is technically incomplete. Is it in base 9 or base 10. It's almost certainly base-10, in which case it is actually base-10 diminished-radix complement. You might look that up.

#### jeoboo

Joined Apr 8, 2017
5
i got it. but i am still confused about number 1. after 1's complement, A becomes 110011.011 and B becomes 111110.100, and then add them, so i got 1110001.111, but i have no idea how to get the correct answer.

i try to convert A and B into decimal and then convert to binary to check my answer.
A=12.5(decimal)
B=1.375(decimal)
-A-B=-13.875(decimal)
and then i convert -13.875 into binary, which is -1101.111(this is correct answer)
and i try to use 2's complement to solve it, i can also get the correct answer.

#### jeoboo

Joined Apr 8, 2017
5
So how might you determine if 110010.111 is the correct answer? What value does it represent in decimal? What value is C in decimal given the values for A and B? Do they agree?

You might consider whether, in general, you can add two 1's complement numbers the same way you add two unsigned binary numbers?

Hint: What are the 4-bit 1's complement representations for 5 and -5? What happens if you add them?

This gets at the very heart of why we use two's complement.

The term "9's complement" is technically incomplete. Is it in base 9 or base 10. It's almost certainly base-10, in which case it is actually base-10 diminished-radix complement. You might look that up.
i tried, but..

#### WBahn

Joined Mar 31, 2012
24,700
i got it. but i am still confused about number 1. after 1's complement, A becomes 110011.011 and B becomes 111110.100, and then add them, so i got 1110001.111, but i have no idea how to get the correct answer.

i try to convert A and B into decimal and then convert to binary to check my answer.
A=12.5(decimal)
B=1.375(decimal)
-A-B=-13.875(decimal)
and then i convert -13.875 into binary, which is -1101.111(this is correct answer)
and i try to use 2's complement to solve it, i can also get the correct answer.