Question

2. Using the sigma (E) notation and given an n-bit sequence of binary digita An-12,-291-3 ... 220,20. what is the value of A if the binary bits are interpreled as: a. an unsigned integer? b. Sign Magnitude number? Page 1 of 3 H. QUAYSON c. Twos Complement number? d. Using the representation of two complement numbers in question 6.c. above, convert the sign-magnitude mmber 1001 into twos complement number. (10 marks)

Answer 1

Solution Ani An-2 An-3 aga, ao nobit binary number. n- Ek let n=4 Co to 15) _ an unsigned integer (o to gne) (sign magnitude number ) (-9 9 ) © det n= 4 to 4-1 4-1 2 to 2 © (-8 to 7) two's complement numbeo - (-ght to 2n-1-1) a's complement 1001 019 Oil (-7)

Solution Ani An-2 An-3 aga, ao nobit binary number. n- Ek let n=4 Co to 15) _ an unsigned integer (o to gne) (sign magnitude number ) (-9 9 ) © det n= 4 to 4-1 4-1 2 to 2 © (-8 to 7) two's complement numbeo - (-ght to 2n-1-1) a's complement 1001 019 Oil (-7)

Modified answer

Sigma Notation @ Unsigned Integer n-1 E ak.dk k=0 b signed Integer n-1 any a n-2 е + E al. 2 1C=0 a's complement * n-2 any 2 + E ak 2 K=0 al : 1001 n=4 Signed Binary Number Az=1, Q2 = 0, 0,=0, QOR! n-1 2 - An-1 + n-2 K' E ak 2 n=0 Az ano + Qoq° + a, 2'+ a222 1x23 + 1x2° + 0x2 + 0x22 - 8+1 Ans