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List the characters (digits) for the following bases. 1) Decimal: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

List the characters (digits) for the following bases. 1) Decimal: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 2) Octal: 0, 1, 2, 3, 4, 5, 6, 7 3) Binary: 0, 1 4) Hexadecimal: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. What base(s) could these numbers represent? (circle those that apply)

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List the characters (digits) for the following bases. 1) Decimal: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

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  1. List the characters (digits) for the following bases. 1) Decimal: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 2) Octal: 0, 1, 2, 3, 4, 5, 6, 7 3) Binary: 0, 1 4) Hexadecimal: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F What base(s) could these numbers represent? (circle those that apply) 5) 4 3 6 7 5 Decimal Octal Binary Hexadecimal 6) 1 7 C 2 D Decimal Octal Binary Hexadecimal 7) 1 0 1 1 1 0 0 1 0 Decimal Octal Binary Hexadecimal 8) 6 1 7 2 8 5 Decimal Octal Binary Hexadecimal 40 40 40 40 40 40 40 40 10 10 What base(s) do these numbers represent? (circle those that apply) 9) 4 3 6 9 510Decimal Octal Binary Hexadecimal 10) 1 7 C 2 D16 Decimal Octal Binary Hexadecimal 11) 1 0 1 1 1 0 0 1 02 Decimal Octal Binary Hexadecimal 12) 6 1 7 2 4 58 Decimal Octal Binary Hexadecimal Add these decimal numbers. (show work) 13) 1 7 9 4 8 2 7 3 ------------- 1 8 2 2 1 14) 1 5 6 8 342 4 6 7 5 ----------6 5 8 5

  2. 11 1 1 1 1 0 1 1 0 1 11 0 1 1 1--------------- ----1 0 0 0 11 1 Carry 1 11---10 10 1---11 1 Carry 1 Add these binary numbers. (show work) 15) 1 0 1 1 0 1 1 0 1 1 ------------- 10 1 2 11 0 1 1 0 1 1 1 0 1 1 1--------------- ----0 10 0 Carry 1 11 1 1 0 1 1 0 1 0 1 0 1 1 1--------------- ----0 0 10 0 Carry 1 3 11 1 1 1 0 1 1 0 1 1 1 0 1 1 0--------------- ----0 0 0 10 0 Carry 1 4 5 6 1 1 1 1 1 1 0 1 1 0 1 0 1 0 1 1 --------------- ----1 10 0 0 1 No Carry 1 1 1 1 1 0 1 1 0 1 1 1 0 1 1 --------------- ----1 1 10 0 0 1 No Carry

  3. 1 2 3 12 6 6 75 3 4 1--------- 0 1 12 6 6 7 6 5 3 4 1 4 --------- --- 0 13 1 1 12 6 6 7 6 5 3 4 1 3 --------- --- 3 0 12 4 5 1 1 1 12 6 6 7 2 5 3 4 1 5 --------- --- 2 3 0 10 1 1 1 1 2 6 6 7 5 3 4 1 ------------1 0 2 3 0 Add these octal numbers. 16) 2 6 6 7 5 3 4 1 ---------- 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 10 11 12 13 14 15 16 17 20 21 etc.

  4. Add these hexadecimal numbers. 17) 2 A 3 4 5 3 F 6 ---------- 0 1 2 3 4 5 6 7 8 9 A B C D E F 0 1 2 3 4 5 6 7 8 9 A B C D E F 10 11 12 13 14 etc. 1 2 3 1 2 A 3 4 35 3 F 6 F---------- -- 2 A 12 2 A 3 4 45 3 F 6 6---------- -- A 2 A 3 4 35 3 F 6 F---------- -- A 12 4 6 5 1 12 A 3 4 A5 3 F 6 3---------- -- 2 A E 1 2 A 3 4 25 3 F 6 5---------- -- E 2 A 7 1 2 A 3 45 3 F 6 ---------- 7 E 2 A

  5. Convert this decimal number to binary. 18) 4 3 2 7 7 0 1 0 1 0 1 0 0 1 0 0 0 0 1 1 0 1 32768 8192 2048 512 128 32 16 8 4 2 1 Positional weight values 65536 16384 4096 1024 256 64 4 3 2 7 7 (remaining number)- 3 2 7 6 8 (largest number not exceeding remainder - 43277) ------------ (mark this bit as ‘on’ = ‘1’) 1 0 5 0 9 (new remaining number) Skip 16384 because it is too large to go into 1 0 5 0 9 (remaining number)Mark position as ‘off’ = ‘0’ 1 0 5 0 9 (remaining number) - 8 1 9 2 (largest number not exceeding remainder - 10509) ------------ (mark this bit as ‘on’ = ‘1’) 2 3 1 7 (new remaining number) Skip 4096 because it is too large to go into 2317 (remaining number)Mark position as ‘off’ = ‘0’ 2 3 1 7 (remaining number) - 2 0 4 8 (largest number not exceeding remainder - 2317) ------------ (mark this bit as ‘on’ = ‘1’) 2 6 9 (new remaining number) Skip 1024 because it is too large to go into 269 (remaining number)Mark position as ‘off’ = ‘0’ Skip 512 because it is too large to go into 269 (remaining number)Mark position as ‘off’ = ‘0’

  6. 2 6 9 (remaining number) - 2 5 6 (largest number not exceeding remainder - 269) ------------ (mark this bit as ‘on’ = ‘1’) 1 3 (new remaining number) Skip 128 because it is too large to go into 13 (remaining number)Mark position as ‘off’ = ‘0’ Skip 64 because it is too large to go into 13 (remaining number)Mark position as ‘off’ = ‘0’ Skip 32 because it is too large to go into 13 (remaining number)Mark position as ‘off’ = ‘0’ Skip 16 because it is too large to go into 13 (remaining number)Mark position as ‘off’ = ‘0’ 1 3 (remaining number) - 8 (largest number not exceeding remainder - 13) ------------ (mark this bit as ‘on’ = ‘1’) 5 (new remaining number) 5 (remaining number) - 4 (largest number not exceeding remainder - 5) ------------ (mark this bit as ‘on’ = ‘1’) 1 (new remaining number) Skip 2 because it is too large to go into 1 (remaining number)Mark position as ‘off’ = ‘0’ 1 (remaining number) - 1 (largest number not exceeding remainder - 1) ------------ (mark this bit as ‘on’ = ‘1’) 0 (new remaining number) Process Completed

  7. Convert this binary number to decimal. 19) 1 0 1 0 1 0 0 1 0 0 0 0 1 1 0 1 1 0 1 0 1 0 0 1 0 0 0 0 1 1 0 1 32768 8192 2048 512 128 32 16 8 4 2 1 16384 4096 1024 256 64 Positional weight values Add the values of the bits that are ‘on’ = ‘1’ 3 2 7 6 8 8 1 9 22 0 4 82 5 6841----------4 3 2 7 7

  8. Convert this binary number to octal. 20) 1 0 1 0 1 0 0 1 0 0 0 0 1 1 0 1 • Separate bits into groups of three (3) • Determine octal number 0 0001 0012 0103 0114 1005 1016 1107 111 1 0 1 0 1 0 0 1 0 0 0 0 1 1 0 1 1 2 4 4 1 5

  9. Convert this binary number to hexadecimal. 21) 1 0 1 0 1 0 0 1 0 0 0 0 1 1 0 1 • Separate bits into groups of four (4) • Determine hex number 0 00001 00012 00103 00114 01005 01016 01107 01118 10009 1001A 1010B 1011C 1100D 1101E 1110F 1111 1 0 1 0 1 0 0 1 0 0 0 0 1 1 0 1 A 9 0 D

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