(a) Convert the following from decimal notation into binary notation: (6 marks) 204.875 (b) Given an eight-position two's complement value box. Use the value box to: (6 marks) (I) convert 10101010 (in base 2) to decimal (II) convert -40 (in base 10) to binary. (c) convert the following binary to hexadecimal then to decimal in sequential steps: (8 marks) 1010111010.11110 (20 Points)
Added by Donald C.
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Step 1
875 from decimal to binary. - Divide 204 by 2 repeatedly and record the remainders from bottom to top: * 204 ÷ 2 = 102 remainder 0 * 102 ÷ 2 = 51 remainder 0 * 51 ÷ 2 = 25 remainder 1 * 25 ÷ 2 = 12 remainder 1 * 12 ÷ 2 = 6 remainder 0 * 6 ÷ 2 = 3 Show more…
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Key Concepts
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Convert each of the following binary numbers to (i) decimal, (ii) octal, (til) duodecimal and (lv) hexadecimal format: (a) $0-10011$ (b) 111001100
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Further problems
1. Convert the following numbers to decimal: a. (101110.11)2 b. (24.28)8 2. Convert the following number to octal and hexadecimal numbers. a. (1101110.11)2 3. Convert the hexadecimal number (68BF)16 to binary and then from binary convert it to octal. 4. Obtain the 1's and 2's complements of the following binary numbers: a. (01111110)2 b. (01111111)2 c. (10000001)2 5. Perform subtraction on the following unsigned binary number using 2's complement of the subtrahend. 111000 - 101010 6. Represent (1091) in BCD. 7. a. Convert the following decimal numbers 60 and 32 to binary using the signed 2's complement representation and enough digits to accommodate numbers. b. Then perform (+60) + (-32)
Samriddhi S.
1. Convert the following binary numbers to decimal: (a) 11012 (b) 10110112 (c) 11112 (d) 1101,01012 (e) 11010,010002 (f) 0000,01012 2. Convert the following decimal numbers to binary (4 decimal places): (a) 50210 (b) 101,21110 (c) 999,37510 (d) 281,00110 (e) 1610 (f) 15,12510 3. Perform the following binary multiplications (Show calculations): (a) 101 x 11012 (b) 11010,01 x 101,102 (c) 110 x 1101,012 (d) 11110 x 10100,0102 4. 110011.112 x 110,1012= ? a) 100110010,011112 b) 101101101,11012 c) 101010110,110112 d) 111100010,1112 5. 11011,10 Ă· 101 (To 4 decimal places). 6. Convert 10011011,00102 to decimal, octal and hexadecimal. 7. Express each of these decimal numbers in 2's complement form (Use 8 Bits): a) 13 b) -13 c) 64.25 d) -64.25
Adi S.
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