Introduction to Number Representation A451 GCSE Computing

BinaryBinary

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.

Bits, Nibbles, Bytes Bit – 1 or 0 Nibble – 4 Bits Byte – 8 Bits

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 =

Converting positive denary integers into binary Example from denary into binary =

1 Byte – Maximum and Minimum Value Maximum value = = 255 Minimum value =

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 =

Hex – Base 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 0*0=0 0*0=0 4*16=64 4*16=64 1*11=11 (B) 1*11=11 (B) 64+11= = B 11

Hex – Base 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) = = *256=2560 (A) 10*256=2560 (A) 14*16=64 (E) 14*16=64 (E) 13*1=11 (D) 13*1=11 (D) = = 2797 AE 14 D 13

Hex to Denary C4 in Hex 1C4 in Hex 1*256 = 256 1*256 = *16 = *16 = 192 4*1 = 4 4*1 = = = 452 1*256 = 256 1*256 = *16 = *16 = 192 4*1 = 4 4*1 = = = 452 1C 4

Hex to Denary EB in Hex EB in Hex 0 * 0 = 0 0 * 0 = 0 16 * 14 = * 14 = * 11 = 11 1 * 11 = = = * 0 = 0 0 * 0 = 0 16 * 14 = * 14 = * 11 = 11 1 * 11 = = = 235 0E B

Binary to Hex in denary 108 in denary  = 6  = 12 (C)  108 in hex is 6C

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 = = =