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DAVJ277 1.2.4
J277 GCSE CS 1.2.4 a) Binary, denary and hexadecimal
| Question | Answer |
|---|---|
| Convert denary numbers 0 - 255 into 8 bit numbers Convert 8 bit numbers into 0 - 255 denary numbers | Use a number line 12864 32 16 8 4 2 1 0 0 1 1 0 1 1 0 = 54 1 0 0 0 1 1 1 0 = 142 1 1 1 1 1 1 1 1 = 255 |
| Add two 8 bit numbers | Use a number line and show carry - left to right 0+0=0, 0+1=1, 1+1=0 carry 1, 1+1+1=1 carry 1 128 64 32 16 8 4 2 1 0 0 1 1 0 1 1 0 54 1 0 0 0 1 1 1 0 142 + 1 1 0 0 0 1 0 0 = 196 |
| Explain Overflow | When there are insufficient bits reserved to store the result of a calculation. Leads to inconsistent result. |
| What is a Binary shift | 1 place Left shift multiplies by 2. 1 place Right shift divides by 2. |
| What arithmetic operation is a 3 place left shift equivalent to? | Multiplying by 8 (1 place left shift multiplies by 2) (2 places left shift multiplies by 4) (3 places left shift multiplies by 8) 2 to the power of the number of places |
| What would the binary and denary equivalent of a one place left shift on 00110011 be? | The binary would be 0110011 0 Denary is 64+32+4+2 = 102 |
| What would the binary and denary equivalent of a two place right shift on 00110011 be? What do you notice about the result? | The binary would be 00001100 Denary is 8+4 = 12 Accuracy is lost as 2 bits have been lost |
| Identify the least significant bit and the most significant bit: 10101101 | The most significant is the bit on the far left (in the largest place value). The least significant bit is the bit on the far right (in the smallest (unit) place value). |
| Convert denary number 0 to 255 into hexadecimal—convert 165 to hexadecimal | Divide by 16 for 1st digit remainder is 2nd. First digit is the DIV, second is the MOD Eg. 165 as hex 165/16 = 10 remainder. 6 = A6 0-9, A=10, B=11, C=12, D=13, E=14, F=15 |
| Convert 2 digit hexadecimal into denary—What is A5 in denary? | 2 digit hex number: 1st column = number of 16s 2nd column = number of Units EXAMPLE 1: A5 hexadecimal = (10 x 16) + (5 x 1) = 160 + 5 = 165 denary EXAMPLE 2: 15 hexadecimal = (1 x 16) + (5 x 1) = 16 + 5 = 21 denary |
| Convert 2 digit hexadecimal into binary—what is A7 in binary? | convert each digit to 4 bit binary then put numbers together. A7 in binary A = 10 in denary = 1001 in 4 bit binary 7 = 0111 in 4 bit binary A7 = 10010111 |
| Convert 8 bit binary to hexadecimal Eg. 10010001 | Split into 2 nibbles so 10010001 becomes 1001 0001 1001 = 9 0001 = 1 Answer in hex =91 |
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Davenant Computer Science
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