1. Introduction to Number Representation A451 GCSE Computing

2. BinaryBinary

3. BinaryBinary All computer processing is carried out digitally. This means that the processor handles instructions as binary codes – zeros and ones. All data on a PC is essentially 0’s and 1’s.

4. Bits, Nibbles, Bytes Bit – 1 or 0 Nibble – 4 Bits Byte – 8 Bits1286432168421 11001100 8421 1010

5. Converting positive denary integers into binary Example 1 Whole positive denary (base ten) numbers are converted into binary as follows: 135 from denary into binary 128 + 4 + 2 + 1 = 135 128643216842110000111

6. Converting positive denary integers into binary Example 2 107 from denary into binary 64 + 32 + 8 + 2 + 1 = 107 128643216842101101011

7. 1 Byte – Maximum and Minimum Value Maximum value = 255 128+64+32+16+8+4+2+1 = 255 Minimum value = 012864321684211111111 1128643216842100000000

8. Hex – Base 16 Only uses single digits Only uses single digits A = 10 A = 10 B = 11 B = 11 C = 12 C = 12 D = 13 D = 13 E = 14 E = 14 F = 15 F = 15 Only uses single digits Only uses single digits A = 10 A = 10 B = 11 B = 11 C = 12 C = 12 D = 13 D = 13 E = 14 E = 14 F = 15 F = 15256161

9. Hex – Base 16 256161 75 in denary 75 in denary is 4B in Hex is 4B in Hex 0*0=0 0*0=0 4*16=64 4*16=64 1*11=11 (B) 1*11=11 (B) 64+11=75 64+11=75 0*0=0 0*0=0 4*16=64 4*16=64 1*11=11 (B) 1*11=11 (B) 64+11=75 64+11=75 0 0 4 64 B 11

10. Hex – Base 16 256161 10 2797 in denary 2797 in denary is AED in Hex is AED in Hex 10*256=2560 (A) 10*256=2560 (A) 14*16=64 (E) 14*16=64 (E) 13*1=11 (D) 13*1=11 (D) 2560+64+11 = 2797 2560+64+11 = 2797 10*256=2560 (A) 10*256=2560 (A) 14*16=64 (E) 14*16=64 (E) 13*1=11 (D) 13*1=11 (D) 2560+64+11 = 2797 2560+64+11 = 2797 AE 14 D 13

11. Hex to Denary 256161 1C4 in Hex 1C4 in Hex 1*256 = 256 1*256 = 256 12*16 = 192 12*16 = 192 4*1 = 4 4*1 = 4 256+192+4 = 452 256+192+4 = 452 1*256 = 256 1*256 = 256 12*16 = 192 12*16 = 192 4*1 = 4 4*1 = 4 256+192+4 = 452 256+192+4 = 452 1C 4

12. Hex to Denary 256161 EB in Hex EB in Hex 0 * 0 = 0 0 * 0 = 0 16 * 14 = 224 16 * 14 = 224 1 * 11 = 11 1 * 11 = 11 0+224+11 = 235 0+224+11 = 235 0 * 0 = 0 0 * 0 = 0 16 * 14 = 224 16 * 14 = 224 1 * 11 = 11 1 * 11 = 11 0+224+11 = 235 0+224+11 = 235 0E B

13. Binary to Hex 01101100 01101100 108 in denary 108 in denary  4 + 2 = 6  8 + 4 = 12 (C)  108 in hex is 6C 01101100 84218421

14. Hex to Binary AF in hex AF in hex (10*16)+(1*15) = 175 (10*16)+(1*15) = 175 A = 10 A = 10 F = 15 F = 15 10101111 = 17510101111 = 175 84218421 10101111