Answer to Question #119200 in Math for Evelyn Teye

Question

compute the value of 410-78 using 8-bit sign magnitude in binary

Answer 1

An 8-bit binary number can have a value ranging from $0 (00000000)_2$ to $255 (11111111)_2$.

78 = $64+8+4+2 = (01001110)_2$.

Hence, 8-bit sign magnitude in binary of -78 is $-78 = (01110010)_2$ .

$410 = 255 + 155 = (11111111)_2 + (10011011)_2$ .

$410-78 = 255 +155-78 = (11111111)_2 + (10011011)_2 + (01110010)_2$ .

Sum will be like that

• 0 + 0 = 0
• 1 + 0 = 1
• 1 + 1 = 10 (binary for 2)
• 1 + 1 + 1 = 11 (binary for 3)

Hence Sum is

$\ \ \ \ \ \ (11111111)_2 \\ \ \ \ \ \ \ (10011011)_2 \\ = (110011010)_2$

So, $255+155 = (110011010)_2$.

Hence,

$410 - 78 = (110011010)_2 + (01110010)_2 = \\ \ \ \ \ (110011010)_2 \\ \ \ + (01110010)_2 \\ = (101001100)_2 = 332$