Convert the following binary numbers to decimal, octal and hexadecimal numbers.
(i) 100101.101
(ii) 10101100.01011
(iii) 1010
(iv) 10101100.010111

Question

Convert the following binary numbers to decimal, octal and hexadecimal numbers. (i) 100101.101 (ii) 10101100.01011 (iii) 1010 (iv) 10101100.010111

KnowledgeBoat · Accepted Answer

(i) 100101.101 Decimal Conversion of integral part: Binary
No | Power | Value | Result ------------ | ----- | ----- | ------ 1 | 2⁰ | 1 | 1x1=1 0 | 2¹ | 2 | 0x2=0 1 | 2² | 4 | 1x4=4 0 | 2³ | 8 | 0x8=0 0 | 2⁴ | 16 | 0x16=0 1 | 2⁵ | 32 | 1x32=32 Decimal Conversion of fractional part: Binary
No | Power | Value | Result ------------ | ----- | ----- | ------ 1 | 2^-1 | 0.5 | 1x0.5=0.5 0 | 2^-2 | 0.25 | 0x0.25=0 1 | 2^-3 | 0.125 | 1x0.125=0.125 Equivalent decimal number = 1 + 4 + 32 + 0.5 + 0.125 = 37.625 Therefore, (100101.101)₂ = (37.625)₁₀ Octal Conversion Grouping in bits of 3: Binary
Number | Equivalent
Octal ---------------- | ------------------- 101 | 5 100 | 4 . | . 101 | 5 Therefore, (100101.101)₂ = (45.5)₈ Hexadecimal Conversion Grouping in bits of 4: Binary
Number | Equivalent
Hexadecimal ---------------- | ------------------- 0101 | 5 0010 | 2 . | 1010 | A (10) Therefore, (100101.101)₂ = (25.A)₁₆ (ii) 10101100.01011 Decimal Conversion of integral part: Binary
No | Power | Value | Result ------------ | ----- | ----- | ------ 0 | 2⁰ | 1 | 0x1=0 0 | 2¹ | 2 | 0x2=0 1 | 2² | 4 | 1x4=4 1 | 2³ | 8 | 1x8=8 0 | 2⁴ | 16 | 0x16=0 1 | 2⁵ | 32 | 1x32=32 0 | 2⁶ | 64 | 0x64=0 1 | 2⁷ | 128 | 1x128=128 Decimal Conversion of fractional part: Binary
No | Power | Value | Result ------------ | ----- | ----- | ------ 0 | 2^-1 | 0.5 | 0x0.5=0 1 | 2^-2 | 0.25 | 1x0.25=0.25 0 | 2^-3 | 0.125 | 0x0.125=0 1 | 2^-4 | 0.0625 | 1x0.0625=0.0625 1 | 2^-5 | 0.03125 | 1x0.03125=0.03125 Equivalent decimal number = 4 + 8 + 32 + 128 + 0.25 + 0.0625 + 0.03125 = 172.34375 Therefore, (10101100.01011)₂ = (172.34375)₁₀ Octal Conversion Grouping in bits of 3: Binary
Number | Equivalent
Octal ---------------- | ------------------- 100 | 4 101 | 5 010 | 2 . | . 010 | 2 110 | 6 Therefore, (10101100.01011)₂ = (254.26)₈ Hexadecimal Conversion Grouping in bits of 4: Binary
Number | Equivalent
Hexadecimal ---------------- | ------------------- 1100 | C (12) 1010 | A (10) . | 0101 | 5 1000 | 8 Therefore, (10101100.01011)₂ = (AC.58)₁₆ (iii) 1010 Decimal Conversion: Binary
No | Power | Value | Result ------------ | ----- | ----- | ------ 0 | 2⁰ | 1 | 0x1=0 1 | 2¹ | 2 | 1x2=2 0 | 2² | 4 | 0x4=0 1 | 2³ | 8 | 1x8=8 Equivalent decimal number = 2 + 8 = 10 Therefore, (1010)₂ = (10)₁₀ Octal Conversion Grouping in bits of 3: Binary
Number | Equivalent
Octal ---------------- | ------------------- 010 | 2 001 | 1 Therefore, (1010)₂ = (12)₈ Hexadecimal Conversion Grouping in bits of 4: Binary
Number | Equivalent
Hexadecimal ---------------- | ------------------- 1010 | A (10) Therefore, (1010)₂ = (A)₁₆ (iv) 10101100.010111 Decimal Conversion of integral part: Binary
No | Power | Value | Result ------------ | ----- | ----- | ------ 0 | 2⁰ | 1 | 0x1=0 0 | 2¹ | 2 | 0x2=0 1 | 2² | 4 | 1x4=4 1 | 2³ | 8 | 1x8=8 0 | 2⁴ | 16 | 0x16=0 1 | 2⁵ | 32 | 1x32=32 0 | 2⁶ | 64 | 0x64=0 1 | 2⁷ | 128 | 1x128=128 Decimal Conversion of fractional part: Binary
No | Power | Value | Result ------------ | ----- | ----- | ------ 0 | 2^-1 | 0.5 | 0x0.5=0 1 | 2^-2 | 0.25 | 1x0.25=0.25 0 | 2^-3 | 0.125 | 0x0.125=0 1 | 2^-4 | 0.0625 | 1x0.0625=0.0625 1 | 2^-5 | 0.03125 | 1x0.03125=0.03125 1 | 2^-6 | 0.015625 | 1x0.015625=0.015625 Equivalent decimal number = 4 + 8 + 32 + 128 + 0.25 + 0.0625 + 0.03125 + 0.015625 = 172.359375 Therefore, (10101100.010111)₂ = (172.359375)₁₀ Octal Conversion Grouping in bits of 3: Binary
Number | Equivalent
Octal ---------------- | ------------------- 100 | 4 101 | 5 010 | 2 . | . 010 | 2 111 | 7 Therefore, (10101100.010111)₂ = (254.27)₈ Hexadecimal Conversion Grouping in bits of 4: Binary
Number | Equivalent
Hexadecimal ---------------- | ------------------- 1100 | C (12) 1010 | A (10) . | 0101 | 5 1100 | C (12) Therefore, (10101100.010111)₂ = (AC.5C)₁₆

Computer Science

Convert the following binary numbers to decimal, octal and hexadecimal numbers.
(i) 100101.101
(ii) 10101100.01011
(iii) 1010
(iv) 10101100.010111

Number System

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Convert the following binary numbers to decimal, octal and hexadecimal numbers.(i) 100101.101(ii) 10101100.01011(iii) 1010(iv) 10101100.010111

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Convert the following binary numbers to decimal, octal and hexadecimal numbers.
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