1 A Perform the following arithmetic in binary assuming 16bi

1 A. Perform the following arithmetic in binary (assuming 16-bit 2’s complement values): (a) 0000 0101 1011 1001 × 0110 0101 (b) 0110 0110 0110 0100 × 1011 1001 (c) 0000 1011 1001 0101 × 0110 1011

b. Perform the following integer arithmetic in binary (assuming 16-bit 2’s complement values): Your answer should have both the quotient and remainder for each problem. (a) 0000 0101 1011 1001 ÷ 0010 0101 (b) 0110 0110 0110 0100 ÷ 0011 1001 (c) 0000 1011 1001 0101 ÷ 0000 1011

Solution

1 a)  (a) 0000 0101 1011 1001 × 0110 0101

  0000 0101 1011 1001 in decimal is 1465

0110 0101 in decimal is 101

After performing Binary Multiplication result is 0010 0100 0001 1111 1101 in decimal is 147965

(b) 0110 0110 0110 0100 × 1011 1001

0110 0110 0110 0100 in decimal is 26212

1011 1001 in decimal is 185

After performing Binary Multiplication result is 0100 1001 1111 1110 0100 0100 in decimal is 4849220

(c) 0000 1011 1001 0101 × 0110 1011

0000 1011 1001 0101 in decimal is 2965

0110 1011 in decimal is 107

After performing Binary Multiplication result is 0100 1101 0111 0100 0111 in decimal is 317255

B) (a) 0000 0101 1011 1001 ÷ 0010 0101

0000 0101 1011 1001 in Decimal is 1465

0010 0101 in Decimal is 37

After performing Binary Division result is

0010 0111.1001 1000 0011 0111 0101 1001 1111 0010 0010 1001 1000 01 in Decimal is 39.5945945945946

(b) 0110 0110 0110 0100 ÷ 0011 1001

0110 0110 0110 0100 in Decimal is 26212

0011 1001  in Decimal is 57

After performing Binary Division result is

0001 1100 1011.1101 1100 0001 0001 1111 0111 0000 0100 0111 1101 11 in Decimal is 459.859649122807

(c) 0000 1011 1001 0101 ÷ 0000 1011

0000 1011 1001 0101  in Decimal is 2965

0000 1011 in Decimal is 11

After performing Binary Division result is

0001 0000 1101.1000 1011 1010 0010 1110 1000 1011 1010 0010 1110 1001 in Decimal is 269.54545454545456