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Convert; 1/2 i) 5210 to binary number (4mks) ii) 10010002 to a denary number (4mks) 2. Given that A= B = and C = . J Determine a single matrix i. Ax B ii. BX A (4mks) iii. The matrix D such that 3D +C = (4mks) K/ D 5 09:25:43 Undo Save

User Giulia
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i. 5210 to binary numberConversion of 5210 to binary numberThe steps for conversion are as follows:Take the decimal number (5210) and divide it by 2.The quotient is 26 and the remainder is 0. Record the remainder. 2 goes into 52, 26 times.Take the quotient from step 1 (26) and divide it by 2.The quotient is 13 and the remainder is 0. Record the remainder. 2 goes into 26, 13 times.Take the quotient from step 2 (13) and divide it by 2.The quotient is 6 and the remainder is 1. Record the remainder. 2 goes into 13, 6 times.Take the quotient from step 3 (6) and divide it by 2.The quotient is 3 and the remainder is 0. Record the remainder. 2 goes into 6, 3 times.Take the quotient from step 4 (3) and divide it by 2.The quotient is 1 and the remainder is 1. Record the remainder. 2 goes into 3, 1 time.Take the quotient from step 5 (1) and divide it by 2.The quotient is 0 and the remainder is 1. Record the remainder. 2 goes into 1, 0 times.Write the remainders from the bottom to the top. The binary number is 1100112. Therefore, 5210 in binary is 1100112.ii. 10010002 to a denary numberConversion of 10010002 to denary numberThe steps for conversion are as follows:Write the binary number with the place value as in the binary number system: 10010002 = 1 × 26 + 0 × 25 + 0 × 24 + 1 × 23 + 0 × 22 + 0 × 21 + 0 × 20.Simplify the above expression: 10010002 = 1 × 64 + 0 × 32 + 0 × 16 + 1 × 8 + 0 × 4 + 0 × 2 + 0 × 1 = 68.Thus, the decimal equivalent of 10010002 is 68.iii. Matrix calculationsGiven that A = B = and C = .To determine the single matrix Ax B we can multiply the matrix A and B. A = B = =C = The matrix D such that 3D +C =K/ D =

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