1. For each problem below, convert the base-10 numbers to binary and then perfor

Question

1. For each problem below, convert the base-10 numbers to binary and then perform the arith- metic on the binary representation of the numbers. Give the result in binary and base-10, where the base-10 value is by interpreting the result as an 8-bit signed integer in two's com- plement. If an overflow or carry occurs, say so. By carry, I am only referring to a carry out of the most significant bits added. Assume each number is an 8-bit signed integer that uses (a) 640 6210 (b) 10010 3010 (c) -7010 +5010 (d 123-1410

Explanation / Answer

a) (64)10 + (62)10

= ( 0100 0000)2

+( 0011 1110)2

---------------------------

(0111 1110)2

=(126)10

b) (100)10+ (30)10

=(0110 0100)2

+(0001 1110)2

------------------------

=(1000 0010)2

=(-126)10

c) (-70)10 + (50)10

=(1011 1010)2 + (0011 0010)2

= 1011 1010

+ 0011 0010

----------------------

1110 1100

=(-20)10

d) (123)10-(14)10

=(0111 1011)2

-(0000 1110)2

------------------------

(0110 1101)2

=(109)10

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